A new hair product possibly needed by a lady (6)
I believe the answer is:
angela
'lady' is the definition.
'a new hair product possibly needed by a' is the wordplay.
'a new' becomes 'an' (I've seen this in other clues).
'hair product possibly' becomes 'gel'.
'needed by' means one lot of letters go next to another.
'an'+'gel'+'a'='ANGELA'
(Other definitions for angela that I've seen before include "girl" , "- Carter, English writer" , "woman" , ". . . Lansbury (actress)" , "Frau Merkel" .)