His first appearance on the stage was at the Theatre Royal, Smock Alley, Dublin, on the 5 February 1744, and his engagement at once increased its prosperity. His first London appearance was made in 1746 as Othello at the Theatre Royal, Drury Lane. Here his talents were speedily recognized, and in Hamlet and Macbeth he alternated with David Garrick, arousing the latter's jealousy by his success as Romeo. This resulted in his leaving Drury Lane for the Covent Garden Theatre in 1750, accompanied by Mrs Cibber, his Juliet. Both houses now at once put on Romeo and Juliet for a series of rival performances, and Barry's Romeo was preferred by the critics to Garrick's.
In 1758 Barry opened the Crow Street Theatre in Dublin, and later a new theatre in Cork. He staged many successful productions but seems to have lived beyond his means. In 1767 returned to London to play at the Haymarket Theatre, then under the management of Foote. As his second wife, he married in 1768 the actress Mrs Dancer (1734–1801), and he and Mrs Barry played under Garrick's management, Barry appearing in 1767, after ten years absence from the London stage, in Othello, his greatest part. In 1774 they both moved to Covent Garden, where Barry remained until his death.