This Lady Hester had a daughter named Hester, Hester Pitt Stanhope.
She was married to the elder William Pitt, PM between 1766 to 1768. According to her Wikipedia article, she was a Baroness in her own right.
From www.findagrave.com. Their image was slightly out-of-focus or otherwise blurred so I added sharpness and changed other settings to bring out available detail. However, the modesty piece and sleeves in the image as found have a pinkish cast.