Cheering up European once argument's resolved (13)
I believe the answer is:
encouragement
'cheering up' is the definition.
'european once argument's resolved' is the wordplay.
'european' becomes 'e' (abbreviation e.g. EU).
'resolved' is an anagram indicator.
'once'+'argument'='onceargument'
'onceargument' is an anagram of 'ncouragement'.
'e'+'ncouragement'='ENCOURAGEMENT'
(Other definitions for encouragement that I've seen before include "Act of spurring on" , "Reassurance, cheer" , "Urging" , "Persuasion" , "Motivation" .)