Her father's Wikipedia article has a good biographical snippet about her. She was succeeded by her daughter Frances Anne.
From invaluable.com.
Anne wears a simple dress, the white color being her emblem of rank along with her pearl bandeau and necklace, in this Mee miniature.
Keywords: 1799, Mee, Anne MacDonnell, Countess of Antrim, MacDonnell family, Vane-Tempest family, Countess, British, curly coiffure, chemise, trapezoidal neckline, close sleeves, criss-cross bodice, vee neckline, strap sleeves, necklace, clasps