Complex sentence: She was initially ballet mistress of American Ballet Theatre, then from 1950 to 1968 taught at the Metropolitan Opera Ballet School, after which she ran her own Manhattan School of Dance until she retired in 1983.
Split into simpler sentences: She was initially ballet mistress of American Ballet Theatre She taught at the Metropolitan Opera Ballet School from 1950--1968. She then ran her own Manhattan School of Dance from 1968 until she retired in 1983.