In 1733 George Stone was made dean of Ferns, and in the following year he exchanged this deanery for that of Derry; in 1740 he became bishop of Ferns, in 1743 bishop of Kildare, in 1745 bishop of Derry, and in 1747 archbishop of Armagh.
These two, afterwards joined by the primate's old rival Lord Shannon, and usually supported by the earl of Kildare, regained control of affairs in 1758, during the viceroyalty of the duke of Bedford.
His grandfather was a small farmer in county Kildare, and his mother was the daughter of a captain in the merchant service.
Conn, who was related through his mother with the earl of Kildare (Fitzgerald), became chief of the Tyrone branch of the O'Neills (Cinel Eoghain) about 1520.
When Kildare became viceroy in 1524, O'Neill consented to act as his swordbearer in ceremonies of state; but his allegiance was not to be reckoned upon, and while ready enough to give verbal assurances of loyalty, he could not be persuaded to give hostages as security for his conduct; but Tyrone having been invaded in 1541 by Sir Anthony St Leger, the lord deputy, Conn delivered up his son as a hostage, attended a parliament held at Trim, and, crossing to England, made his submission at Greenwich to Henry VIII., who created him earl of Tyrone for life, and made him a present of money and a valuable gold chain.