[2] Gibney was raised on the family farm in Killygorman townland, parish of Kildallan, County Cavan.

Gibney studied for the priesthood at the preparatory seminary at Stillorgan and from 1857 at the Catholic Missionary College of All Hallows in Drumcondra, Dublin.

Gibney entered the burning building in an attempt to rescue anyone inside, and found the bodies of gang members Joe Byrne, Dan Kelly and Steve Hart, as well as the mortally wounded hostage Martin Cherry, who he helped retrieve and to whom he gave the last rites.

His episcopate was marked by a number of poor investment decisions as the diocese purchased shops, offices, houses, and a hotel in Perth as well as a newspaper, exerting editorial influence by banning the publication of horse racing information, which led to the paper's eventual demise.

[2] During his episcopate he was closely involved with the founding of the Beagle Bay Aboriginal community north of Broome, along with what eventually became St John of God Health Care.