Sotheby’s notes refer to her as Lady Nasmyth and state, "The sitter was married to Sir James Nasmyth of Posso…” A check of thepeerage shows this could be Sir James Naesmyth of Posso, 3rd Bt who married Eleanor Murray in 1785. This portrait could date to about the time of their marriage, the coiffure being in keeping with that time. The keywords below are for Eleanor Murray.
From Sotheby’s Web site.