Favour reduction of violence initially during outrage (8)
I believe the answer is:
approval
'favour' is the definition.
(winning favour is winning approval)
'reduction of violence initially during outrage' is the wordplay.
'initially' suggests taking the first letters.
'during' means one lot of letters goes inside another.
'outrage' becomes 'appal' (synonyms).
The initial letters of 'reduction of violence' is 'rov'.
'rov' inserted into 'appal' is 'APPROVAL'.
(Other definitions for approval that I've seen before include "Blessing" , "Favourable judgement" , "Commendation - on which to try things out" , "Acceptance as satisfactory" , "On it, goods may be returned if not satisfactory" .)