Stephens was a star of the British stage, although his only significant film lead was the title role in Billy Wilder's The Private Life of Sherlock Holmes (1970). Early on, Stephens acted in repertory and small parts in film and television, but first gained notice as the title character in Epitaph for George Dillon on the West End and then on Broadway in 1958. In 1963, Laurence Olivier invited him to join the National Theater Company, playing Horatio in Hamlet and later leading roles such as Atahualpa in The Royal Hunt of the Sun. In film, he had a principal role in A Taste of Honey and supporting parts in Cleopatra (with Elizabeth Taylor) and Morgan! (with David Warner). He worked with Franco Zefferelli on stage (as Benedick in Much Ado About Nothing, reprised for TV) and in film (the prince in Romeo and Juliet). In Much Ado and other stage and film roles, he played opposite Maggie Smith, who he married. They worked together on-screen in The Prime of Miss Jean Brodie and Travels with My Aunt.
Stephens starred in the horror film The Asphyx and in the miniseries Vienna 1900 (1973). Stephens' career began to decline, following a break with Olivier, the end of his marriage to Smith, and struggles with alcohol. He continued to work in television, with major supporting roles as Uncle Kurt in the miniseries Holocaust, and on radio (playing King George III in a historical drama and Aragorn in the BBC version of The Lord of the Rings). He was a regular on the short-lived sitcom Hell's Bells (as the Bishop), continued in miniseries (The Box of Delights, War and Remembrance), and guest starred on Inspector Morse. As the 1980s wore on, his career improved, appearing in mainstream films High Season, Steven Spielberg's Empire of the Sun, and Kenneth Branagh's Henry V (as Pistol). Around the same time, he made a stage comeback, joining the Royal Shakespeare Company in 1991 and playing Julius Caesar, Falstaff (in both parts of Henry V), and King Lear. Film work continued, mostly cameos in The Bonfire of the Vanities (publisher Sir Gerald Moore), Charlie Chaplin (ironically as a drunk), and Searching for Bobby Fischer (as a rival's chess teacher). He was knighted in 1995 and died later that year.