Fanciful female academic's claim (7)
I believe the answer is:
profess
This clue is a double definition.
'fanciful female academic's' is the first definition.
(whimsically, a female prof)
'claim' is the second definition.
(I know this)
(Other definitions for profess that I've seen before include "State insincerely" , "Affirm faith in (religion)" , "Declare openly" , "State openly" , "Make open declaration of" .)