Redmond is best known in the United States for her role as Sister Jacqueline in the situation comedy The Flying Nun starring Sally Field, which aired on ABC from 1967 to 1970.
She has made guest appearances on television programs ranging from Ben Casey in 1962 through Law & Order in 1997; other credits include a recurring role in Matlock, two appearances (as different characters) on The Munsters, and single-episode appearances on The Donna Reed Show, The Rockford Files, Murphy Brown, Mama's Family and many others.
Redmond played sage innkeeper Sarah Tucker in television commercials for Cool Whip dessert topping in the 1970s.
Redmond's film roles are fewer than her television appearances. They include a small part in 1961's Sanctuary (from William Faulkner's novel, and a remake of the better-remembered The Story of Temple Drake), an appearance (playing Sister Liguori, prefiguring her Flying Nun role) in The Trouble with Angels, and a supporting role in Alfred Hitchcock's Family Plot, which starred Karen Black and Bruce Dern. Her most recent film was 1993's Manhattan Murder Mystery, directed by Woody Allen.
Redmond's theatrical experience ranges from appearing with Nancy Walker in the 1955 revue Phoenix '55 to understudying Angela Lansbury in the original Broadway production of Stephen Sondheim's Sweeney Todd. She played a supporting role in the 1981 Broadway production of Ronald Harwood's The Dresser, which starred Tom Courtenay.
In 1999, Redmond appeared Off-Broadway in Joan Vail Thorne's sentimental comedy The Exact Center of the Universe. The Village Voice noted Redmond's presence among the "old pros" in the cast (which also included Frances Sternhagen), calling her performance "solid and funny".