Murray is educated at St. Patrick’s Teacher Training College in Drumcondra, Dublin. He works as a schoolteacher and in 1900 is appointed headmaster of the national school in Rathduff, County Cork. His first play, The Wheel of Fortune, is produced in 1909 by the Little Theatre in Cork, a theatre he had co-founded with Daniel Corkery, Con O’Leary and Terence MacSwiney. The play is revised and renamed Sovereign Love in 1913. In 1915, he moves to Dublin as headmaster of the Model Schools at Inchicore, where he remains until his retirement from teaching in 1932.
Murray’s play Birthright is performed in the Abbey Theatre in 1910 and establishes him as a writer of force. In all, he writes fifteen plays, all of which are produced by the Abbey. His two most highly regarded works are Maurice Harte (1912) and Autumn Fire (1924). Both of these and Birthright are performed in New York City on Broadway, with Autumn Fire having a run of 71 performances. He also writes an autobiographical novel Spring Horizon (1937).
It has been stated both by A. DeGiacomo and by R. Allen Cave that, in the Art competitions at the 1924 Summer Olympics in Paris, France, Murray is awarded a bronze medal for his play Birthright. However, according to the official record for the games, although Murray is a participant in the literature category with this play and also with Maurice Harte, he does not win a medal.
T. C. Murray dies in Dublin on March 7, 1959.