Lieutenant-Governor and Chancellor of the Isle of Man through the inquiry of 1791 and 1792.

He took the oath at Castle Rushen on 7 January 1791, swearing to deal truly and uprightly between the King and his subjects within the Isle, and as indifferently between party and party as the staff of office then stood. His appointment allowed the resignation of Richard Dawson, who had been Lieutenant-Governor under Governor Smith, to be accepted that year.

The Commissioners of Inquiry worked through him. Their requisitions for information came to the House of Keys by way of the Lieutenant-Governor, and the Keys resolved that their answers should go back by the Speaker to him, to be laid before the Commissioners. His own letters are printed among the Commissioners' papers alongside those of Deemster Moore, the Attorney-General Sir Wadsworth Busk, the Clerk of the Rolls and the Speaker of the Keys. One of them is a character reference, describing its subject as a gentleman of honour, of integrity and respectable talents, a lawyer by profession and among the first as well as the seniors of the bar.

Thomas Stowell inscribed his Statutes and Ordinances of the Isle of Man of 1792 to him as Lieutenant-Governor and Chancellor. He was still in office in 1793, when an Act of Tynwald which had received the royal assent, signified in a letter directed to him of 22 June, was promulgated on the Tynwald Hill on 22 July, and he signed the attestation after the Duke of Atholl. Later lists give the government of 1798 as the Duke of Atholl and Alexander Shaw jointly.