Boasting supporter facing bother about volume (7)
I believe the answer is:
bravado
'boasting' is the definition.
(I've seen this before)
'supporter facing bother about volume' is the wordplay.
'supporter' becomes 'bra' (a bra gives support to breasts).
'facing' means one lot of letters go next to another.
'bother' becomes 'ado' (both can mean fuss or commotion).
'about' says to put letters next to each other.
'volume' becomes 'v' (abbreviation for volume in book titles).
'ado' after 'v' is 'vado'.
'bra' next to 'vado' is 'BRAVADO'.
(Other definitions for bravado that I've seen before include "front" , "A show of boldness or bluster" , "Rash display of courage" , "A show of boldness, may be phoney" , "Show of bravery" .)