I could find nothing about her and very little about her husband. The engraving was done by Charles Wilkin after a Hoppner portrait.
From Wikimedia.
Lady Rancliffe wears something similar to the chemise a la reine of ten years earlier in this 1795 Hoppner portrait.
Keywords: 1795, Hoppner, Wilkin, Elizabeth Anne Parkyns, James family, Parkyns family, Baroness, British, long curly coiffure, feathered cap, trapezoidal neckline, modesty piece, flounces, long tight sleeves, cuffs, waist band, natural waistline, full skirt, necklace, gloves