Robert D'Arcy, 3rd Earl of Holdernesse (1681-1721), was the son of the Hon. John D'Arcy and his wife Bridget, daughter of Robert Sutton, 1st Baron Lexington. He succeeded his grandfather, Conyers, 2nd Earl of Holdernesse, as the 3rd Earl of Holdernesse, on the latter's death in 1692, his father having died earlier that year. In 1702 he was appointed Constable of Middleham Castle, an office his grandfather had held. He was later appointed Lord Lieutenant of the North Riding (1718); President of the Board of Trade (1718); and Lord of the Bedchamber (1719). He married Federica, daughter and co-heir of Meinhardt, 3rd Duke of Schomberg, and his wife Caroline Elisabeth, daughter of Charles-Louis, Elector Palatine. He died at Bath in 1721 and was buried at Hornby Castle.
This picture has previously been identified as a portrait of William Henry, Earl of Ancram, on the basis of the inventory number on the portrait's frame which relates to the Leeds inventory of 1902 (op.cit.), in which it is identified as such. This, however, seems unlikely on the basis of the inclusion of an earl's coronet in the portrait to which the Earl of Ancram was not entitled.