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 Seán O'Casey's The Silver Tassie. His first stage appearance was in 1939 in New York City 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.