Handle European making complaint (5)
I believe the answer is:
gripe
'complaint' is the definition.
(an objection or source of annoyance)
'handle european' is the wordplay.
'handle' becomes 'grip' (synonyms).
'european' becomes 'e' (abbreviation e.g. EU).
'grip'+'e'='GRIPE'
'making' acts as a link.
(Other definitions for gripe that I've seen before include "Complain; colic (water)" , "beef" , "Complain, grouse" , "Protest" , "Grievance" .)