I cannot absolutely identify the sitter, but this may be Mary Murray whose Wikipedia article has some interesting items: "Lady Elizabeth Mary Murray (1760–1825) was a British aristocrat.
Murray was born on 18 May 1760 in Warsaw, Poland. She was the daughter of David Murray, 2nd Earl of Mansfield (1727–1796) by his first marriage to Henrietta Frederica von Bünau. Her maternal grandfather was Count Heinrich von Bünau (1697–1762).
Following her mother's death in 1766, she was brought up at Kenwood House by her father's uncle William Murray, 1st Earl of Mansfield and his wife Elizabeth. They soon also took in their great-niece Dido Elizabeth Belle (1761-1804), the mixed-race natural daughter of Murray's nephew, Sir John Lindsay ; he sent the young Dido to his uncle from the West Indies.
She married George Finch-Hatton (1747–1823) on 10 December 1785. They had three children...”
This image, from liveinternet.ru/users/steampunk3d/post326615557/, was posted 16 November 2016 replacing one titled,"Marchioness of Rockingham by George Romney (location unknown to gogm)” that came from thepeeragethat misidentifies the sitter as Anne Finch, the First Marchioness of Rockingham. But that Ann Finch died in 1761 while this Lady sports a 1780s coiffure.