Born and ordained in Ireland, Killian moved to Australia, where he became Bishop of Port Augusta before succeeding Robert Spence as Archbishop of Adelaide.

During his time as Bishop of Port Augusta, Killian would travel over large distances to visit the scattered parishes of the rural diocese.

Killian's tenure as archbishop saw Adelaide host the National Catholic Education Congress in 1936, in part as a contribution to the celebrations of the South Australian colony's centenary.

[1][3][4] When reflecting on his time as archbishop, Killian listed the conference as one of his proudest achievements, along with the re-opening of Mary MacKillop's school and convent in Penola.

[3] In the last year of his life, Killian suffered from cancer, and on 28 June 1939 he died while undergoing surgery[5] in St Vincent's Private Hospital Melbourne.