Kirkland joined the New York City Ballet in 1968 at age 15. She was promoted to soloist in 1969, and principal in 1972. She went on to create leading roles in many of the great twentieth century ballets by Balanchine, Jerome Robbins, and Antony Tudor. She appeared in Balanchine's revival of "The Firebird", Robbins' "Goldberg Variations", and Tudor's "The Leaves are Fading". She left the New York City Ballet to join the American Ballet Theatre in 1974.