In 1794 he was created Baron Dundas, of Aske in the North Riding of the County of York, in the Peerage of Great Britain.

[3] Lord Dundas notably purchased the right to the earldom of Orkney and lordship of Zetland from James Douglas, 14th Earl of Morton.

He also represented Richmond and York in Parliament and served as Lord Lieutenant of the North Riding of Yorkshire.

At first a Liberal, he held minor office in the second administration of William Ewart Gladstone but later joined the Conservative Party and served from 1889 to 1892 as Lord Lieutenant of Ireland.

There are additional heirs in remainder to the earldom, barony and baronetcy descended from the younger brothers of the first marquess.