The city could face an exodus of seasoned school leaders this summer because of a perk in the new principals-union contract that will reward new retirees.

Members of the Council of School Supervisors and Administrators who retire by June 30 can collect their retroactive pay, which could be as much as $50,000, all at once. If they wait any longer, they won’t see a lot of that money until 2020 and 2021 — a setup likely to incentivize a larger-than-average number to leave this summer, just as Chancellor Carmen Fariña has put a new emphasis on the importance of experienced school leaders.

City officials won’t say how many school leaders are eligible for retirement or how many they expect to leave, though the number could be sizable. Half of city principals in 2013 were 48 or  older — the minimum retirement age is 55 — and teacher retirements jumped by 50 percent last spring after teachers were offered a similar perk in their contract.

Some school leaders who have fought the urge to retire for years said the new contract may be enough to push them over the edge. Celina Napolitano could have retired 12 years ago, but is now in her third year as a principal at Brooklyn’s P.S. 23. After 39 years in the system, Napolitano said she is seriously considering retirement but remains conflicted.

“The engine is just starting to roll here,” she said of the school.

In recent years, the city has lost between 60 and 70 principals to retirement annually, and city officials acknowledged that number could rise this year, though they expected the increase to be small. Research has shown that high principal turnover has an adverse effect on academic gains, particularly in struggling schools.

Eric Nadelstern, a former city education official who now runs a principal training program at Teachers College, said an increase in retirements could bring difficulties for the city. This year’s crop of prospective leaders will likely be large enough, he said, but Fariña’s new regulation that new principals have at least seven years of experience has already shrunk their numbers somewhat.

“The seven-year experience requirements coupled with a huge potential exodus is a formula for serious problems come next fall,” said Nadelstern.

But in some ways, the city is more prepared than ever to deal with principal-hiring challenges.

When Chancellor Joel Klein took over in 2002, he inherited one problem — a massive principal shortage — and faced another self-imposed one. Klein and his successor Dennis Walcott opened more than 400 schools, an endeavor that created thousands of vacancies over the years. In the last four years alone, the city hired 790 new principals and 1,600 new assistant principals, according to the Wallace Foundation. (No new schools are opening this year.)

Klein launched a training academy to prepare and certify a new wave of principals to fill the surge in vacancies. In the years since, the city has spun off more of its own programs, all of which focus on recruiting, training and supporting prospective and beginner leaders.

“The system at that time was not prepared to deal with that level of turnover,” said Jody Spiro, director of education leadership at the Wallace Foundation, which funds several leadership training programs run by the Department of Education. “That’s a huge contrast to today.”

The retirement picture will get clearer in the coming months, said CSA spokeswoman Anne Silverstein. CSA members have for years been expected to give 90 days notice to avoid “a jolt to the system,” Silverstein said.