Singer under the control of the hypnotist Svengali, and a hat (6)
I believe the answer is:
trilby
(Other definitions for trilby that I've seen before include "one by du Maurier?" , "Man's hat or girl hypnotised by Svengali" , "It was felt to provide capital cover" , "du Maurier's heroine" , "Book by George du Maurier - hat" .)