Claim made by little old female in crowd (7)
I believe the answer is:
profess
'claim' is the definition.
(professing is a kind of claiming)
'little old female in crowd' is the wordplay.
'little' says to take the initial letters.
'in' means one lot of letters goes inside another.
'crowd' becomes 'press' (press is a kind of crowd**).
The first letters of 'old female' is 'of'.
'of' placed into 'press' is 'PROFESS'.
'made by' acts as a link.
(Other definitions for profess that I've seen before include "Affirm faith in (religion)" , "Claim or declare" , "Affirm, acknowledge" , "Make open declaration of" , "State insincerely" .)