Redmond may be best known as Sister Jacqueline in The Flying Nun, which aired on ABC from 1967-70. She was nominated for an Emmy for Outstanding Supporting Actress in a Comedy Series for her Sister Jacqueline role during the 1967-68 season but lost to Marion Lorne, who won posthumously for her role as "Aunt Clara" on Bewitched. She made guest appearances on television programs ranging from Ben Casey (1962) through Law & Order (1997). She made a guest appearance on Perry Mason in 1965 as Henrietta Hull in "The Case of the Mischievous Doll". Other credits include a recurring role as Mrs. McCardle in Matlock, two appearances (as different characters) on The Munsters, and one time appearances on Barnaby Jones, Quincy M.E., The Cosby Show, The Sandy Duncan Show, Ryan's Hope, The Donna Reed Show, The Rockford Files, Murphy Brown, and Mama's Family, among others.