Supporter of British Royal Academy (3)
I believe the answer is:
bra
'supporter' is the definition.
(a bra gives support to breasts)
'british royal academy' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in BBC).
'royal academy' becomes 'RA'.
'b'+'ra'='BRA'
'of' is the link.
(Other definitions for bra that I've seen before include "one carrying chest" , "I give a couple a lift" , "Female undergarment" , "Underwear item" , "support" .)