Trendy cool hat is childish (9)
I believe the answer is:
infantile
'childish' is the definition.
('infantile' can be a synonym of 'childish')
'trendy cool hat' is the wordplay.
'trendy' becomes 'in'.
'cool' becomes 'fan' (I've seen this in other clues).
'hat' becomes 'tile' (I've seen this before).
'in'+'fan'+'tile'='INFANTILE'
'is' is the link.
(Other definitions for infantile that I've seen before include "Inflate in childish way" , "in early stage of development" , "for kids" , "Babyish" .)