His aim was to secure political power, a desire which brought him into conflict with Henry Boyle, the Speaker of the Irish House of Commons, who had organized a formidable opposition to the government.

The archbishop was one of the "undertakers" who controlled the Irish House of Commons, and although he did not regain the almost dictatorial power he had exercised at an earlier period, which had suggested a comparison between him and Cardinal Wolsey, he continued to enjoy a prominent share in the administration of Ireland until his death, which occurred in London on 19 December 1764.

He constantly favoured a policy of conciliation towards the Roman Catholics, whose loyalty he defended at different periods of his career both in his speeches in the Irish House of Lords and in his correspondence with ministers in London.

[1] Philip Stanhope, 4th Earl of Chesterfield told him that he was the only man with the political skills to rule Ireland, but in a dig at his irregular private life, said that it would help if he became a clergyman.

Horace Walpole, who gives a generally unfavourable picture of his private character, acknowledges that Stone possessed "abilities seldom to be matched", and gives him credit for charity, generosity and an absence of malice; and he had the distinction of being mentioned by David Hume as one of the only two men of mark who had perceived merit in that author's History of England on its first appearance.