One assumes the bowl of fish and stretched paw is a reference to Thomas Gray's "Ode on the Death of a Favourite Cat, Drowned in a Tub of Gold Fishes" (1748). That light verse plays with 18th century assumptions about women:
What female heart can gold despise?
What cat's averse to fish?
This particular portrait is in the National Portrait Gallery and has been since 1929 when John Baring, 2nd Baron Revelstoke (banking money) made it a gift. The Baron enjoyed his respectability rather longer.