Both Christie's and Sotheby's have handled this portrait. Christie's lot notes follow: "Emma Gilbert (1729-1807) was the only child of John Gilbert, Archbishop of York, and his wife Margaret Sherard. In 1761 she married George, 3rd Baron Edgecumbe, later 1st Mount Edgecumbe, a close friend of Reynolds, whose name appears in the artist's pocket book for numerous social engagements (see D. Mannings, Sir Joshua Reynolds: A Complete Catalogue of his Paintings, London, 2000, pp. 175-6).
The present portrait is likely to date to circa 1758, before the sitter's marriage. Reynolds painted her again in 1762, three-quarter-length, but the picture was destroyed by bombing in World War Two. Northcote recorded an anecdote in his Life of Reynolds that Lady Edgcumbe was 'uncommonly plain or rather ugly in her person, [and] when she was sitting to Reynolds [told him]:'I do not know what you may think of my face for a picture, but this I know, that it is no common face', [and Reynolds replied] 'Thank God it is not'. (See D. Mannings, loc. cit., fig. 553, p.175)."
Her article in thepeerage is here.
Image from the-athenaeum; vertical streak-like flaws throughout the image, but especially the background removed with Photoshop by gogm.