He was ordained a priest and became chaplain to the Spanish Embassy in London in 1767 and rector of the attached chapel.  He became friendly with the politician Edmund Burke and the writer Dr. Johnson and other notable people and he was regarded as one of the ablest and best informed men of his time. He was elected a fellow of the Royal Society in 1792.  When Spain allied itself to France on the side of the American colonies, Hussey stayed on at the embassy after the ambassador had returned to Madrid and was then sent to Madrid by George III to detach Spain from the alliance.  His mission failed but his abilities as a diplomat were recognised. He took up the Catholic cause earnestly and was deputed by the English Catholics to go to Rome to lay their position before the Pope, but the Spanish embassy would not grant him leave of absence.  King George III, Pitt, and the Duke of Portland entrusted him with a mission to the Irish soldiers and militia in Ireland who were disaffected, but when he heard their story, he pleaded on their behalf much to the distaste of the Irish executive.  

He helped to establish the Catholic seminary at Maynooth, County Kildare, and he became its first president in 1795. Two years later he was appointed Bishop of Waterford and Lismore, despite the divisions, on his appointment, among the clergy of the diocese (he was considered to be the 'Castle' nominee) and he was consecrated in Francis Street Chapel, Dublin.  Hussey governed his see from his residence in Gracedieu in the city, unlike his predecessors who had lived in Clonmel or Carrick-on-Suir.  It was then (1797) that he issued the famous Pastoral letter published by James Ramsey of Waterford, to his clergy, strongly resenting Government interference in ecclesiastical discipline. This protest gave great offence to the ministers and it caused a fierce political storm.  

It is said that he helped to frame the Concordat of 1802 between Napoléon and Pope Pius VII.   He died at Tramore, County Waterford, 11 July 1803  - he took a fit while swimming - and his funeral on July 12th, "Orangeman's Day", caused a sensation in the city.  As the funeral was proceeding up the Quay towards the "Big Chapel", a group of drunken English soldiers, who had been commemorating "King Billy" at an Orange meeting, attacked the funeral and attempted to throw the coffin into the river.   This desecration of the remains was prevented only after a stern defence was put up by the mourners and the riot was eventually quelled by the arrival of the local militia.