Nora Koreff began taking dance lessons at the Metropolitan Opera Ballet School at the age of eight. At age 15 she joined the Met's corps de ballet, and, after further training under Michel Fokine (Fokine, Michel) and George Balanchine (Balanchine, George), she joined the Ballet Theatre (now American Ballet Theatre) at its formation in 1939. By then she had altered her surname to Kaye. For a time in the later 1930s she became interested in Broadway and danced in a number of musical productions, including Virginia (1937), Great Lady (1938), and Stars in Your Eyes (1939).

Kaye's first substantial character role was in Antony Tudor's Gala Performance in February 1941. Other small parts followed in various works, but in April 1942 she burst into the ranks of prima ballerinas with her performance as Hagar in the world premiere of Tudor's Pillar of Fire. As Ballet Theatre's leading dramatic ballerina, she subsequently danced major roles in Tudor's Lilac Garden and Dim Lustre, Balanchine's Waltz Academy (premiered October 1944), Bronisława Nijinska's Harvest Time, and Jerome Robbins (Robbins, Jerome)'s Facsimile (premiered October 1946), among others. The leading role of Agnes de Mille (de Mille, Agnes)'s Fall River Legend had been choreographed with Kaye in mind, but illness delayed her dancing it until after the premiere in April 1948. Other productions in which she starred included Fokine's Petrouchka, Balanchine's Theme and Variations, and Tudor's Nimbus.

In February 1951 Kaye joined the New York City Ballet, with which she appeared in Robbins's The Cage (premiered June 1951) and Age of Anxiety and Tudor's La Gloire (premiered February 1952). In 1952 she also appeared in Bette Davis's Broadway revue Two's Company, with choreography by Robbins. From 1954 to 1959 she was again with the renamed American Ballet Theatre, where she danced in Winter's Eve, Journey, and Paean.

Kaye saw herself as a very American ballet dancer, compelled to question the traditions, interpretations, and movement of ballet. In 1959 Kaye married choreographer Herbert Ross, with whom the next year she formed the Ballet of Two Worlds, a company that presented Ross's Angel Head, Rashomon Suite, and The Dybbuk. She retired from performing in 1961. In 1964 she was named assistant to the director of the American Ballet Theatre, and she served as the associate artistic director from 1977 to 1983. She and her husband produced the motion picture The Turning Point in 1977 and collaborated again in 1987 on Ross's film Dancers.