Barbarism's not in fashion (7)
I believe the answer is:
outrage
'barbarism's' is the definition.
(thesaurus)
'not in fashion' is the wordplay.
'not in' becomes 'out' ('out' is the opposite to 'in').
'fashion' becomes 'rage' (rage is a kind of fashion**).
'out'+'rage'='OUTRAGE'
(Other definitions for outrage that I've seen before include "Violate" , "A feeling of righteous anger" , "Shock grossly" , "Fury" , "Barbarity" .)