Free complaints about arrogance (4-10)
I believe the answer is:
self-importance
'arrogance' is the definition.
(thesaurus)
'free complaints about' is the wordplay.
'about' is an anagram indicator.
'free'+'complaints'='freecomplaints'
'freecomplaints' with letters rearranged gives 'SELF-IMPORTANCE'.
I've seen this clue in The Daily Express.
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