Beginning his career with a long run with the Royal Shakespeare Company, Stewart received the 1979 Laurence Olivier Award for Best Actor in a Supporting Role for his performance in Antony and Cleopatra in the West End.
Memulai kariernya dalam jangka panjang dengan Royal Shakespeare Company, dia menerima Laurence Olivier Award 1979 untuk Aktor Terbaik dalam Peran Pendukung atas penampilannya di Antony and Cleopatra di West End.