Suffer trendy dog (5)
I believe the answer is:
incur
'suffer' is the definition.
(to incur is to suffer or experience)
'trendy dog' is the wordplay.
'trendy' becomes 'in' ('in' can mean fashionable).
'dog' becomes 'cur' (both can mean a despicable person).
'in'+'cur'='INCUR'
(Other definitions for incur that I've seen before include "Run up" , "Invite, bring about" , "Take on (obligation)" , "Provoke" , "Become responsible for" .)