Educated at the Christian Brothers schools in Dublin, he later attended at University College, Dublin and initially read medicine before moving into drama.
Redmond was one of four children born to cabinet-maker Thomas and Eileen Redmond. They had four children. Redmond was invited to join the Abbey Theatre in 1935 as a producer by William Butler Yeats, the Irish poet.
Yeats wrote his play Death of Cuchullain for Redmond to star as Cúchullain, hero of one of Ireland"s foundational myths.
Redmond made his acting debut at the Abbey Theatre in 1935 in Sean O"Casey"s The Silver Tassie. His first stage appearance was in 1939 in New York in The White Steed.
After returning to Britain at the outbreak of the Second World War he was a regular on the London stage. He was one of the founders of WAAMA, the Writers", Artists", Actors" and Musicians" Association, a precursor of Irish Actors" Equity.
His insistence that "part-time professionals" – usually civil servants who acted on the side – should be paid a higher rate than professional actors for both rehearsal time and performance, effectively wiped out this class, raising the wages and fees of working actors.
Redmond worked in television and film throughout the 1950s to the 1980s and was regularly seen in television series such as The Avengers, Daniel Boone, The Saint and Z-Cars. He was often called upon as a character actor in various military, religious and judicial roles in films such as I See a Dark Stranger (1946), Captain Boycott (1947), High Treason (1951), The Cruel Sea (1953), Playboy of the Western World (1962), Kid Galahad (1962), The Luck of Ginger Coffey (1964), Tobruk (1967), The Ghost and Mr. Chicken (1966) and Barry Lyndon (1975).
His performance as the kindly occult expert in the cult horror film Night of the Demon (1957) is a favourite of fans of the film.
Redmond retired to Dublin and died aged 76 after a long period of ill health in 1989.