From the moment that he became Primate of All Ireland, Stone proved himself more a politician than an ecclesiastic. "He was said to have been selfish, worldly-minded, ambitious and ostentatious; and he was accused, though very probably falsely, of gross private vice." 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 Duke of Dorset's reappointment to the Lord Lieutenancy in 1751, with his son Lord George Sackville as Chief Secretary for Ireland, strengthened the primate's position and enabled him to triumph over the popular party on the constitutional question as to the right of the Irish House of Commons to dispose of surplus Irish revenue, which the government maintained was the property of the Crown.
When Dorset was replaced by the Duke of Devonshire in 1755, Boyle was raised to the peerage as Earl of Shannon and received a pension, and other members of the opposition also obtained pensions or places; and the archbishop, finding himself excluded from power, went into opposition to the government in alliance with John Ponsonby. 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. In the same year Stone wrote a remarkable letter, preserved in the Bedford Correspondence (ii. 357), in which he speaks very despondingly of the material condition of Ireland and the distress of the people. 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. According to Horace Walpole, his death was due to ruining his constitution by an excess of food and alcohol.
Although this "much-abused prelate," as Lecky calls him, was a firm supporter of the English government in Ireland, he was far from being a man of tyrannical or intolerant disposition. It was due to his influence that in the anti-tithe disturbances in Ulster in 1763 the government acted with conspicuous moderation, and that the movement was suppressed with very little bloodshed. He constantly favored 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. Philip Stanhope, 4th Earl of Chesterfield told him that he was the only man with the political skill to rule Ireland, but in a dig at his irregular life, said it would help if he became a clergyman.
Archbishop Stone, who never married, was a man of remarkably handsome appearance; and his manners were "eminently seductive and insinuating." Richard Cumberland, who was struck by the "Polish magnificence" of the primate, speaks in the highest terms of his courage, tact, and qualities as a popular leader. Horace Walpole, who gives an unfavourable picture of his private character, acknowledges that Stone possessed "abilities seldom to be matched", and give him credit for charity and generosity; 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. He was himself the author of several volumes of sermons which were published during his lifetime.