Hinds began his professional acting career at the Glasgow Citizens' Theatre in a production of "Cinderella" (1976). He remained a frequent performer at the Citizens' Theatre during the late 1970s and through the mid-1980s. During this same period, Hinds also performed on stage in Ireland with the Abbey Theatre, the Field Day Theatre Company, the Druid Theatre, the Lyric Players' Theatre and at the Project Arts Centre. In 1987, he was cast by Peter Brook in "The Mahabharata", a six-hour theatre piece that toured the world, and he also featured in its 1989 film version. Hinds almost missed the casting call in Paris due to difficulties renewing his Irish passport. In the early 1990s, he was a member of the Royal Shakespeare Company.