Lincoln Center for the Performing Arts, which has operated without a permanent leader since April, has chosen a new president and chief executive from the academic world: Debora L. Spar, the president of Barnard College.

Ms. Spar, 53 years old, will be the first woman to lead the performing-arts organization, whose 16-acre campus is home to arts groups such as the Metropolitan Opera and New York City Ballet.

Her...