Born in London, Clay studied at the Royal Academy of Dramatic Art (RADA) and began his acting career in the early 1970s with small parts in film and television. He and also appeared in several West End theatre productions. He was cast in several of Laurence Olivier's Old Vic productions and during the decade 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 most widely seen screen performance was as Lancelot in the 1981 film Excalibur, and he also appeared in the film versions of D. H. Lawrence's Lady Chatterley's Lover (1981), and Agatha Christie's Evil Under the Sun (1982), the latter reuniting him with his The Misanthrope co-star Diana Rigg.

He continued working regularly on stage and appeared in a number of made for television movies and mini-series. In the last years of his life he taught drama at the Actors Centre and the Academy of Live and Performing Arts, and also worked in association with RADA, generally in the role of promoting the organisation, or providing advice to acting students.

He died of cancer in London.