Clay appeared in several West End theatre productions. He was cast in several of Laurence Olivier's Old Vic productions and during the 1970s came to be regarded as one of British theatre's most promising actors. Among his successes was The Misanthrope, which led Clay to the United States, where he also played this role on Broadway in 1975.

His early films included the cult thriller The Night Digger (1971) and The Darwin Adventure (1972) in which he portrayed the young Charles Darwin. In 1981 he gave his most widely-seen screen performance, as Lancelot in the 1981 film Excalibur. He also appeared in Just Jaeckin's film version of D.H. Lawrence's Lady Chatterley's Lover (1981), playing Mellors, and in Agatha Christie's Evil Under the Sun (1982), the latter reuniting him with Diana Rigg, his co-star in The Misanthrope.

He appeared as Alan in the 1976 version of The Picture of Dorian Gray, alongside Peter Firth. In 1978 he played Henry Wriothesley, 3rd Earl of Southampton in the drama series Will Shakespeare, about the life of Shakespeare.

In 1983 Clay appeared as Stapleton in a version of The Hound of the Baskervilles. Two years later he appeared in another Sherlock Holmes adaptation in the role of Doctor Percy Trevelyan in an episode of The Adventures of Sherlock Holmes entitled "The Resident Patient". He also appeared in the UK ITV series Gentlemen and Players in 1988-89.

Clay continued working regularly on stage and appeared in a number of made-for-television films and miniseries. In 1984 he played Mike Preston in the Hammer House of Mystery and Suspense episode "Child's Play".

In 1992 he appeared with Kim Thomson in the BBC TV series Virtual Murder, and played Lord Leo in the 1998 TV miniseries Merlin starring Sam Neill. His final screen appearance was in Roger Ashton-Griffiths' short film And Beyond.

Clay married Actress Lorna Heilbron in 1980. He died of liver cancer in London on 25 May 2000. He was survived by his wife, his daughters, Ella (born 1983) and Madge (born 1986), and his mother, Rose.