She was Lettice Knollys' daughter and great granddaughter of Mary Boleyn. Her private life was fraught with conflict and intrigue as described here and here. She is usually considered to be the inspiration for Stella in Sir Phillip Sidney's Astrophel and Stella sonnets.
Penelope Devereux appears to be wearing an attifet-like headdress and French farthingale with hanging sleeves in this portrait. She also wears a pendant on the sleeve to right. In the portrait, the openings of the hanging sleeves and the edges of her revers are highlighted in orange.