[2] He was drama captain of St Ignatius' College, Riverview in Sydney in 1964, where, like Gerard Windsor and Justin Fleming, he was taught by Melvyn Morrow.

During 1971 and 1972 Enright was a member of Sydney's Genesian Theatre, performing in A Doll's House and Uncle Vanya, and directing London Assurance.

His many plays include: Good Works, Blackrock, Daylight Saving, Mongrels (about the relation between Australian playwrights Jim McNeil and Peter Kenna, the latter a friend), The Female Factory, A Man with Five Children, On the Wallaby, and A Poor Student, many of them published by Currency Press.

He wrote the book and lyrics to a number of musical works: three musicals with Terence Clarke – The Venetian Twins; Variations (Winner, NSW Premier's Literary Play Award, 1983); and Summer Rain (commissioned for a graduating class at NIDA) -, and others with Alan John (Orlando Rourke), David King (The Betrothed, The Voyage of Mary Bryant, The Good Fight), and Max Lambert (Miracle City); and an opera with Graham Dudley (The Snow Queen).

Enright wrote the book of the stage musical version of The Boy from Oz, based on the biography of the same name written by Stephen MacLean, which was produced by Ben Gannon with great success around Australia, and, after his death, in New York.

Enright had been appointed an adjunct professor in the School of Drama at the Western Australian Academy of Performing Arts; after his death, one of his former WAAPA students, Eddie Perfect, wrote an elegiac song about him ('Someone Like That').