Under Mr. VanBesien and Mr. Gilbert, the orchestra expanded its programming and reached more single-ticket buyers with innovative events, including the NY Phil Biennial, a new music festival, and its popular “Art of the Score” series, in which the orchestra plays the scores of films as they are screened. But selling tickets to one concert a time drives up marketing costs, and it is difficult to make up for the loss of subscribers who once bought packages of many concerts each season. Mr. VanBesien expanded the orchestra’s horizons outside New York, establishing partnerships with cultural institutions in Shanghai, Santa Barbara, and Michigan, among others.

Officials had hoped to release the proposed designs for the new hall this fall but decided that they needed more time to study the project, which was proving more complex than some had initially imagined. Ms. Farley said that the team also hoped to get a better sense of its projected costs and whether the construction could really be completed in just two seasons. The tentative date for opening the rebuilt hall has been pushed back a year, to the fall of 2022.

Mr. VanBesien got to know his new home, the University Musical Society, well when the Philharmonic began a five-year residency partnership there in 2015. He said he had been drawn by its diverse programming; this season’s offerings include both the Berlin Philharmonic and Simon McBurney’s immersive theater piece “The Encounter.”

He will become the seventh president in its 138-year history, succeeding Kenneth C. Fischer, who expanded its ambitions in his three decades in the position.

“It’s been a big decision for me, and I’ve had a few sleepless nights on top of the regular sleepless nights I have in this position, but in the end this was a really special opportunity,” Mr. VanBesien said in a recent interview, adding that he also hoped to achieve a better work-life balance when he starts in July. “I’m not leaving because I am angry,” he added. “I’m not leaving because I’m miserable or something like that, or that I’m so frustrated. I’m going because I think for me, personally, this makes a lot of sense.”

Oscar S. Schafer, the chairman of the Philharmonic’s board, noted that the donations made so far had come before people had even seen the designs. “When we have schematics ready in the fall, we’ll have something to show these people,” he said.

Peter W. May, the board’s vice chairman, credited Mr. VanBesien with strengthening the orchestra’s management team, but said that he was confident that the orchestra could continue its fund-raising without him and Ms. Mantone. “I don’t think there’s going to be any lag,” he said. “We really don’t think we’re going to miss a beat.”