Brought in from outside the arts, Ms. Spar is leaving after a rocky year. Lincoln Center dramatically scaled back plans to rebuild David Geffen Hall; ended one of its summer mainstays, the Lincoln Center Festival; endured tensions between longtime senior staff and members of Ms. Spar’s new team; and grappled with financial challenges, projecting a deficit this year.

Her departure comes only six months after the decision to scuttle the expensive gut renovation of Geffen Hall, the New York Philharmonic’s home at the center, and seek simpler ways to improve it. When Ms. Spar, who started a $400 million capital campaign at Barnard, took over, the plans for the hall were considerably more ambitious, with most of the money needed for the project — estimated at more than $500 million — still to be raised.

But in October, Lincoln Center and the Philharmonic, spooked by the rising price tag and projections that the orchestra would need to leave the hall for several years during construction, announced they were drastically scaling back. It was a major setback for a project that has been mulled for nearly 20 years, and threw cold water on the fire finally ignited by a $100 million gift from the entertainment mogul David Geffen in 2015. After the decision to abandon the gut renovation, Mr. Geffen expressed frustration at the lack of additional support for the project from other wealthy donors.

Lincoln Center has insisted the more minimal plan is not an admission of failure. “We’ve got some great plans that everyone is very excited about,” Katherine Farley, Lincoln Center’s chairwoman, who led the center and oversaw the Geffen Hall rebuilding plans for almost a year between Mr. Bernstein’s departure and Ms. Spar’s arrival, said in an interview.

The revision of the hall’s plans was driven by Deborah Borda, the powerful arts leader who was named president and chief executive of the Philharmonic last year. In an interview, Ms. Borda disputed the idea that there was a clash between her and Ms. Spar.