Grace made his theatrical debut in weekly rep in Frinton-on-Sea in 1969, and appeared in Trevor Peacock's Erb later that year, which transferred to the Strand Theatre in Spring 1970, his first appearance in the West End. He joined the Royal Shakespeare Company in 1972, and in 1973 played Aumerle there in the Ian Richardson/Richard Pasco Richard II (which transferred to Broadway). Back at the RSC from 1976-8 he appeared as Dromio of Ephesus in Trevor Nunn's first ever musical, The Comedy of Errors (with Judi Dench, Michael Williams and Roger Rees), Hitler in Schweik and Witwoud in The Way of the World, directed by John Barton.
He played Hamlet for the opening of Derby Playhouse in 1975.
He filmed Brideshead Revisited from 1979 to 1981, and following the success of that programme played Richard II at the Young Vic in 1981, and Mozart in Amadeus with Frank Finlay at Her Majesty's Theatre in 1982. He then began working in operetta, playing Koko in The Mikado and Joseph Porter in HMS Pinafore for Sadler's Wells Opera in repertoire from 1982-1986.
The film Heat and Dust followed in 1983. Other theatre includes Jenkins' Ear by Dusty Hughes at the Royal Court in 1986, Bernstein's Candide (Old Vic/Scottish Opera/BBC) in 1988/9 and The Mystery of Irma Vep at the Leicester Haymarket (1990), which transferred to the Ambassadors Theatre. He played Cole Porter in A Swell Party at the Vaudeville in 1991/2 and appeared in Ken Russell's production of Princess Ida for ENO at the Coliseum in 1992.
In the "official biography" of the actor Alan Bates, Otherwise Engaged: The Life of Alan Bates, by Donald Spoto (published on 7 June 2007), Spoto quotes Grace describing his "'intense affair'" with Bates, who was "terrified of exposure": "'I told him labels didn't matter, but that we must be who we are. But he just could not accept that. Alan was at ease as long as he pretended - and he insisted on pretending - that our relationship was not what it was, and was not disclosed to or evident to others.'"
He has a recurring role in some Doctor Who audio plays, produced by Big Finish as a Time Lord ally of the Eighth Doctor and Lucie Miller, opposite Paul McGann and Sheridan Smith in the plays Human Resources, Sisters of the Flame and Vengeance of Morbius.