Childish supporter wears trendy hat (9)
I believe the answer is:
infantile
'childish' is the definition.
(I know that childish can be written as infantile)
'supporter wears trendy hat' is the wordplay.
'supporter' becomes 'fan' (fan is a kind of supporter).
'wears' means one lot of letters goes inside another.
'trendy' becomes 'in' ('in' can mean fashionable).
'hat' becomes 'tile' (old-fashioned term for a hat).
'in'+'tile'='intile'
'fan' placed inside 'intile' is 'INFANTILE'.
(Other definitions for infantile that I've seen before include "for kids" , "Babyish" , "Inflate in childish way" , "in early stage of development" .)