Enright was born in Shinrone, County Offaly in 1940. He was educated at the Cistercian College, Roscrea, University College Dublin and the Incorporated Law Society of Ireland. He practised as a solicitor before becoming involved in politics in 1967 as a member of Offaly County Council for the Birr Local electoral area. Enright was first elected to Dáil Éireann as a Fine Gael Teachta Dála (TD) for the Laois–Offaly constituency at the 1969 general election. He was subsequently appointed Fine Gael spokesperson on Tourism (1977–1979) and Consumer Affairs (1979–1981).
Enright lost his Dáil seat at the 1992 general election to Pat Gallagher as part of the swing to the Labour Party in that election. He was then elected to the 20th Seanad, where he served from 1993–97. He regained his Dáil seat at the 1997 general election and retired at the 2002 general election. He was succeeded by his daughter Olwyn Enright.
|Party political offices|
| Chairman of the Fine Gael parliamentary party