Broadcast favouring assertion (8)
I believe the answer is:
proclaim
'broadcast' is the definition.
(thesaurus)
'favouring assertion' is the wordplay.
'favouring' becomes 'pro' (I've seen this in other clues).
'assertion' becomes 'claim' (claim is a kind of assertion).
'pro'+'claim'='PROCLAIM'
(Other definitions for proclaim that I've seen before include "Make a public announcement" , "Broadcast" , "advertise" , "Speak out" , "Announce officially or declare publicly" .)