The sitter was the third son of Archibald, 9th Earl of Eglinton. He succeeded to the Earldom in 1769 on the death of his elder brother, Alexander, and joined the army as a young man. When Pitt began to form regiments of Highlanders at the outset of the Seven Years War, he raised a regiment, numbered as the 77th foot, which he took to America. After much adventurous service, it was disbanded in 1764, after which he was appointed Colonel of the 51st foot. He was successively appointed Major-General, in 1772, Lieutenant-General in 1777, and Governor of Edinburgh castle in 1782. He married twice: first, in 1772, Lady Jean Lindsay, eldest daughter of George, 18th Earl of Crawford, who died childless, and second, in 1783, Frances, only daughter of Sir William Twysden, 6th Bt., of Roydon Hall, Kent, by whom he had two daughters. On his death, in 1796, he was succeeded by a kinsman, Hugh Montgomerie, in the title, while most of the family estates passed to his elder daughter, Lady Mary. The title and the estates were, however, reunited with the marriage of Lady Mary to Archibald, Lord Montgomerie, eldest son of the 12th Earl, in 1803.
Lord Eglinton is recorded as having sat to Reynolds on 24 and 27 March and 6 April 1784. This is likely to have been for a full-length in Highland dress for which Reynolds made a preparatory drawing. A payment of 88.19s by Lord Eglinton also seems to have been made in November 1783 (ledgers in the Fitzwilliam Museum, II). The payment seems unlikely to have been for the full-length as the sittings had not by then been completed. Another unfinished portrait of the sitter, head and shoulders, 30 x 25in., in the Royal Collection may be a preliminary study for the full-length or it is possible the full-length was never finished and came into the collection of King George IV perhaps already partly cut down.