Thepeerage has an article for Mary La Zouche here. It says she lived between 1512 and 1542. Wikipedia has an article for Anne Gainsford here. However, the caption for another e-version of this same portrait states "Hans Holbein chalk portrait of a woman whom some art historians identify as Anne Gainsford; however, it's more likely to be that of Mary Zouche, another lady-in-waiting. The name M. Souch in the top left corner of the portrait could indicate either Mistress Zouche or Mary Zouche." Anne Gainsford married Sir George Zouche. The Royal Collection calls this "Mary Zouche?" and dates it between ca. 1532-43.