Revere made her Broadway debut in 1931 in The Great Barrington. Three years later, she went to Hollywood to reprise her stage role in the film adaptation of Double Door. She returned to Broadway to create the role of Martha Dobie in the original 1934 production of The Children's Hour, and in later years she appeared on the New York stage in As You Like It, The Three Sisters, and Toys in the Attic, for which she won the 1960 Tony Award for Best Performance by a Featured Actress in a Play.