Agree aunt breaks promise (9)
I believe the answer is:
guarantee
'promise' is the definition.
(guaranteeing is a kind of promising)
'agree aunt breaks' is the wordplay.
'breaks' is an anagram indicator.
'agree'+'aunt'='agreeaunt'
'agreeaunt' is an anagram of 'GUARANTEE'.
(Other definitions for guarantee that I've seen before include "Written assurance, pledge" , "security system" , "Underwrite; promise with certainty" , "Ensure" , "Assurance, warranty" .)