She studied ballet with Bronislava Nijinska, one of Diaghilev's choreographers (whose most famous work was the original Rite of Spring), and made her professional debut in 1940 dancing for Nijinska at the Hollywood Bowl. In 1942, Colonel de Basil, director of the Ballets Russes de Monte Carlo, invited her to join his company, according to the Times.

In 1945, she married Oleg Tupine, a Ballets Russes star; the two also danced together. In 1948, Clare joined Sergei Denham's competing Ballet Russe company as a principal dancer, performing leading roles in classics such as Les Sylphides, Copp_lia and The Nutcracker.

In 1958, after her dancing career was ended by a knee injury, Clare founded Ballet La Jeunesse, a prominent training company in Los Angeles. She was the school's director and choreographer until the late 1980s, after which she became active as a guest teacher and arts lecturer. George Balanchine sometimes gave classes at the school; he also authorized the company's use of several of his important works, according to the Times.

Born in 1919 in Los Angeles, Clare was the daughter of Lilian Mettler and Paul H. "Scoop" Conlon, a Hollywood agent, publicist and former reporter at The Los Angeles Times.

Clare's autobiography, Behind the Tutu, was published in 2004.