In 1879 he entered the Catholic Missionary All Hallows College in Dublin to study for the priesthood, sponsored for the Diocese of Goldburn, Australia.

[3] In 1911 he was nominated Bishop of Perth and received episcopal ordination from Cardinal Patrick Moran on 17 March 1911.

[4] Clune with his strong support for the Great War and conscription in Australia, would have been seen as pro-British, had met with and gained the trust of Lloyd George, returned to Dublin incognito as "Doctor Walsh", he met with Arthur Griffith (acting president of the republic and Sinn Féin while De Valera was in America) in Mountjoy Jail and then Michael Collins who was voted by the Dail to act as president while Griffith was in prison.

Clune's meeting with the Irish republican leadership was arranged by Bishop Fogarty of Killaloe, Bishop in Clune's native County Clare, who had served as vice-president on Maynooth to the then president and future Archbishop of Melbourne, Daniel Mannix who was known for his nationalist strong sympathies.

[2] His remains were exhumed in June 2013, and reinterred in the crypt of St Mary's Cathedral Perth in September 2013.