Complex sentence: His first play to be professionally produced was "The Big Birthday Suit", which was mounted by the Abbey Theatre in Dublin in 1956, and his plays were produced regularly after that by Dublin's most prestigious theatres.
Split into simpler sentences: His first play to be professionally produced was "The Big Birthday Suit", which was mounted by the Abbey Theatre in Dublin in 1956. After that his plays were produced regularly by Dublin's most prestigious theatres.