When the Trump Organization sold its interest in a public golf course in New York City to Bally’s, the deal was freighted with symbolism.

Bally’s promptly erased the giant “Trump Links” sign from the property in the Bronx by the Whitestone Bridge. Suddenly, a visible artifact of President Trump’s despised presence in New York was gone, and Bally’s — one of several bidders hoping to win one of three coveted casino licenses up for grabs in the state — took credit.

The ceremony in 2024 created the impression of an irrevocable separation between the Bally’s bid and the Trump Organization. But the two in fact remain intertwined.

If Bally’s were to win a casino license, it would have to pay the Trump Organization $115 million, according to the companies’ purchase agreement. That is on top of the $60 million Bally’s already paid the Trump Organization to acquire the remainder of its lease for the city-owned golf course.

The agreement with Bally’s was referenced in the New York attorney general’s civil fraud case against Mr. Trump and his family business, but has received little publicity.

Bally’s and the Trump Organization made the agreement before Mr. Trump’s second term, but the payout would come while he is president, and as he considers countless issues affecting the finances and governance of New York State and New York City. The state is running the casino siting competition, with input from local elected officials, including Mayor Eric Adams.

The mayor frequently says he would like a casino in New York City, but has declined to endorse a particular bidder. Even so, he may have a vested interest in helping Mr. Trump, whose Justice Department is seeking dismissal of the mayor’s federal corruption case.

The mayor’s press secretary, Kayla Mamelak Altus, falsely accused The New York Times of implying that Mr. Adams was pushing for a specific casino and having done so before.

“This marks the second casino bid The New York Times has incorrectly implied the mayor is putting his weight behind, so perhaps the paper should make up its mind before falsely implying there’s a third,” she said in a statement.

Bally’s is one of at least 11 contenders that have expressed interest in bidding for one of the three downstate gambling licenses. Several of the other bidders have ties to Mr. Trump.

Steven Cohen, the Mets owner who wants to build a casino next to the team’s stadium in Queens, donated $1 million to Mr. Trump’s first inaugural committee. The family of Miriam Adelson, one of Mr. Trump’s biggest supporters, controls Las Vegas Sands, which is bidding to build a casino on Long Island.

But none of the other bids, if successful, would seem to directly benefit Mr. Trump. The casino bids are due in June, with the state saying it will make a decision by the end of the year.

In an interview, Soo Kim, the chairman of Bally’s, described the agreement with the Trump Organization as a “a deferred purchase price mechanism,” and said it was an agreement that he did not come to lightly.

“When they first proposed it, I was like, ‘What the hell?’” said Mr. Kim on Tuesday. “They’re already getting a lot of money for a golf course. What do they think it’s worth? But they know what it’s worth to me and to us and to the Bronx.”

The Trump Organization, Mr. Kim said, agreed to transfer the lease on the condition that it would get more money if the land was approved for a casino.

A spokeswoman for the Trump Organization did not immediately respond to a request for comment.

Assemblyman Michael Benedetto, a Democrat whose Bronx district includes the golf course, dismissed the prospect of a $115 million Trump payout as merely “a contractual agreement made by two businesses” and said it would not influence whatever decision he ultimately makes about supporting the casino bid.

“People were just happy to get rid of the name ‘Trump’ from the golf course,” he said. “It was an embarrassment to the community.”

This week, Mr. Benedetto and State Senator Nathalia Fernandez said they had introduced legislation that would enable Bally’s to operate a casino on the golf course, should it win a license. Any such legislation is expected to require a home rule message, a message of support from the New York City Council.

Lincoln Restler, the Brooklyn councilman who chairs the committee that would have to advance that home rule message, said that elected officials were likely to look askance at any deal that would enrich the president’s company.

“I think that a $115 million check to the Trump Organization will be a difficult pill for many New York legislators to swallow,” Mr. Restler said.

The $115 million payout was mentioned in a scathing ruling that a New York State judge issued in the civil fraud case against Mr. Trump and the Trump Organization. In that case, which was brought by Letitia James, the state’s attorney general, the judge imposed a more than $450 million judgment against Mr. Trump, concluding he had fraudulently inflated his net worth to dupe banks into giving him favorable loans.

The judge, Arthur F. Engoron, referred to the golf course deal as giving the Trump Organization a “windfall profit.”

Mr. Trump is appealing Justice Engoron’s ruling.

Ben Protess and Jonah E. Bromwich contributed reporting.

In New York, playing to voters’ concerns about crime has become a popular strategy, successful enough that even left-leaning Democrats have embraced calls for more police officers.

Zohran Mamdani, a democratic socialist rising in the polls in the New York City mayor’s race, has chosen a different approach.

His 18-page public safety plan, which will be released on Tuesday, does not call for hiring more police officers, as several of his rivals have done. Mr. Mamdani, a state assemblyman from Queens, would instead create a city agency called the Department of Community Safety that would focus on expanding violence interrupter programs and mental health teams that respond to 911 calls.

“The police have a critical role to play,” he said in an interview. “Right now, we’re relying on them to deal with the failures of our social safety net. This department will pioneer evidence-proven approaches that have been successful elsewhere in the country.”

Mr. Mamdani said he also would eliminate the Police Department’s huge overtime budget and a unit known as the Strategic Response Group that responds to protests.

His criminal justice platform is likely to appeal to his supporters on the left. But some voters appear to be tilting away from progressive theories on reducing crime. The city moved to the right in the presidential election in November after President Trump portrayed the city as crime-ridden and raised concerns about violence by immigrants.

Most of the candidates in the Democratic mayoral primary have taken more centrist positions on policing. Crime has fallen in the city in recent years after a pandemic spike, yet felony assaults remain high and many New Yorkers worry about violence on the subway.

Former Gov. Andrew M. Cuomo, who leads in mayoral polls, has argued that the city is in crisis and said he would hire 5,000 more police officers. He has criticized candidates who supported the “defund the police” movement, including Mr. Mamdani, who called for reducing the police budget when he was an Assembly candidate in 2020.

Brad Lander, the left-leaning city comptroller, has said he would keep the current police commissioner, Jessica Tisch, and hire hundreds of police officers. Zellnor Myrie, a state senator who was once pepper sprayed by the police, wants to hire 3,000 officers.

The Police Department is facing a staffing crisis as officers quit and it struggles to replace them. It has about 34,100 officers, down from a peak of 40,000 in 2000, according to department figures and the city’s Independent Budget Office.

Civil rights groups and progressive elected officials have long called for a more expansive view of public safety that goes beyond policing and focuses on reducing poverty and addressing mental health problems. They have criticized stop-and-frisk policing and supported the use of violence interrupters, who try to defuse disputes before they escalate.

Mr. Mamdani, who has risen to second place in the polls, has been a strong fund-raiser and has released popular plans for free buses and city-owned grocery stores.

He, too, said he would consider keeping Ms. Tisch as police commissioner and praised some of her policies, including addressing concerns about corruption and reducing the size of the department’s communications staff.

His proposed Department of Community Safety would have a budget of roughly $1 billion, comprising $600 million for existing programs and $450 million in new funding. It would be run by a commissioner-level position, and Mr. Mamdani would eliminate the deputy mayor for public safety, a role that Mayor Eric Adams revived in 2022.

He would expand programs like the Behavioral Health Emergency Assistance Response Division, or B-Heard, which sends teams of mental health professionals, rather than the police, to certain emergencies. He also wants to deploy “mental health navigators” in neighborhoods and outreach teams at 100 subway stations to connect people with services.

Mr. Mamdani said that he would pay for the additional costs related to the new agency — and for his broader affordability proposals — by raising taxes on wealthy residents and large corporations and through a better use of existing city funds and stronger enforcement of tax policy.

It seems clear that Mr. Cuomo intends to attack his left-leaning rivals for favoring progressive approaches over what he considers more pragmatic solutions, especially concerning public safety.

When Mr. Mamdani, Mr. Lander, Mr. Myrie and a fourth candidate, the City Council speaker, Adrienne Adams, were backed by the left-leaning Working Families Party on Saturday as part of the group’s initial endorsement, Mr. Cuomo’s team had a quick response.

Rich Azzopardi, a spokesman for the Cuomo campaign, called the four Democrats a “fringe group of extremists who brought us anti-Israel, ‘defund the police’ and other failed policies that have brought our city to the brink.”

Mr. Adams, a former police officer, successfully campaigned in 2021 on a vow to improve public safety. He brought back contentious police units that focus on removing guns from the streets but have also contributed to a rise in illegal police stops.

Mr. Mamdani said that Mr. Adams had promised as a candidate to bring down crime and to reform the Police Department, but then “betrayed” voters by focusing only on the first issue.

“Democratic primary voters prefer a comprehensive approach with fully funded treatment programs and gun violence prevention and a focus on outcomes,” he said.

Alana Sivin, a director at the Vera Institute of Justice, a criminal justice nonprofit, said that Mr. Mamdani’s plan embraced the “full range of tools” that are needed to improve public safety and “successful precedent in other parts of the country,” including the Community Safety Department in Albuquerque, N.M., which has responded to more than 82,000 calls for service.

Maria Cramer contributed reporting.

Claire Shipman is only days into her job as acting president of Columbia University but is already being targeted by a prominent House Republican who questions her commitment to fighting antisemitism on campus.

Ms. Shipman, in a private text message in December 2023 to Nemat Shafik, who was then Columbia’s president, referred to congressional hearings into campus antisemitism as “capital hill nonsense,” according to a transcript of the exchange released by the House Committee on Education and the Workforce as part of an investigative report last year.

The comment is coming back to haunt Ms. Shipman. Representative Elise Stefanik, who is remaining in the House after President Trump withdrew her nomination to be U.S. ambassador to the United Nations, seized on the remark during a television interview Sunday, predicting that Ms. Shipman will not last long in her new position.

“It’s already come out that she has criticized and belittled the House investigation and the accountability measures and has failed to protect Jewish students,” Ms. Stefanik said on Fox News’s “Sunday Morning Futures.”

“It’s untenable for her to be in this position, and I think it is only going to be a matter of weeks before she’s forced to step down as well,” she added.

On X, Ms. Stefanik, whose pointed questioning of Ivy League presidents about antisemitism during the committee hearings sparked the departures of the presidents of Harvard and the University of Pennsylvania, gave other details.

She wrote that last April, when Ms. Shipman testified alongside Dr. Shafik at the committee hearings into antisemitism, Ms. Shipman had “cheered in the back anteroom about how it was going so well for them,” even as a pro-Palestinian encampment on Columbia’s lawns was forming that same day.

In the related fallout, Dr. Shafik resigned in August, and Dr. Katrina Armstrong, her interim replacement, left her post on Friday.

“Two Presidents later, here we are,” Ms. Stefanik posted on Saturday. “They will be onto yet another Columbia President very, very soon after this one. They still don’t get it.”

The federal government’s Task Force to Combat Antisemitism pulled about $400 million in federal research grants from Columbia on March 7. A week later, it issued a letter outlining nine steps it wanted Columbia administrators to take as a precondition to start negotiations about returning the money.

Dr. Armstrong pledged to comply with the conditions in a letter sent to the federal government on March 21. But a week later, after media reports that she had played down the extent of the changes at a private faculty meeting, Columbia announced that she was stepping down. The board of trustees selected Ms. Shipman as her acting replacement until a permanent president could be hired.

In her private text to Dr. Shafik in December 2023, Ms. Shipman showed an interest in engaging the pro-Palestinian movement rather than disciplining it. She suggested that Columbia “think about how to unsuspend the groups” — a reference, the report said, to Students for Justice in Palestine and Jewish Voice for Peace, two student groups that had been suspended for repeatedly violating university rules.

She also suggested working with Rashid Khalidi, a Palestinian historian, now retired, who was affiliated with Columbia’s Center for Palestine Studies. In the House committee’s description, this amounted to “working behind the scenes to appease the University’s antisemitic actors.”

“FINDING: COLUMBIA’S LEADERS EXPRESSED CONTEMPT FOR CONGRESSIONAL OVERSIGHT OF CAMPUS ANTISEMITISM,” the report trumpeted over its description of Ms. Shipman’s text message.

A Columbia spokeswoman, Samantha Slater, said on Monday that the university was proceeding with the changes it had promised, which include empowering a unit of campus police with arrest powers and increasing oversight of a Middle East studies department.

“We are focused on doing what is right and honoring our commitments to create a Columbia community where students are safe and able to flourish,” she said in a statement. “This will secure Columbia’s future.”

Ms. Shipman, who has been on the Columbia board since 2013 and became co-chair in 2023, did not address the controversy Monday in her first formal letter introducing herself to the campus in her new role. But she said she would follow through on Columbia’s pledge to address the Trump administration’s concerns.

“We will continue to build on the significant progress we’ve made, and the plan outlined to move our community forward,” she wrote.

“My request, right now, is that we all — students, faculty, staff, and everyone in this remarkable place — come together and work to protect and support this invaluable repository of knowledge, this home to the next generation of intellectual explorers, and this place of great and continuing promise,” Ms. Shipman wrote.