Announced main assumption (9)
I believe the answer is:
principle
'assumption' is the definition.
(thesaurus)
'announced main' is the wordplay.
'announced' shows a homophone (sound like).
'main' becomes 'principal' (synonyms).
'principal' is a homophone of 'PRINCIPLE'.
(Other definitions for principle that I've seen before include "In which, theoretically" , "Rule of personal conduct" , "honour" , "Set of rules" , "General scientific law" .)