Big-headed artist many women have a use for (3)
I believe the answer is:
bra
'a use for' is the definition.
The definition suggests a singular noun which matches the answer.
'big-headed artist many women' is the wordplay.
I cannot really see how this works, but
'artist' could be 'ra' (Royal Academician, member of Royal Academy of Arts) and 'ra' is located in the answer.
A single letter 'b' remains which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'have' is the link.
Can you help me to learn more?
(Other definitions for bra that I've seen before include "support" , "Underwear item" , "one carrying chest" , "Chest supporter" , "I give a couple a lift" .)