He is best known for taking part in talks with Richard Cumberland in an attempt to arrange a peace treaty between Spain and Britain during the American War of Independence.
He attracted widespread attention in 1797 by issuing a pastoral letter to his clergy that strongly resented government interference in ecclesiastical discipline and the proselytising of Protestants in Ireland by the establishment of religious schools.
Hussey officially opened the first monastery and school of Edmund Ignatius Rice at Mount Sion in Waterford on July 7, 1803.
Hussey's remains were brought back to Waterford for burial, but his funeral became the focus of sectarian violence.
During the funeral procession to the Great Chapel, the coffin and Hussey's mourners were set upon by a group of drunken soldiers returning from an Orange Order meeting.
The men abused the mourners and attempted to throw Bishop Hussey's remains into the River Suir, which runs through Waterford.
A riot broke out, and the local militia were forced to intervene and recover the remains, which were eventually interred in the Great Chapel, as originally intended.