Local banks are almost right for account (9)
I believe the answer is:
narrative
'for account' is the definition.
(narrative is a kind of account)
'local banks are almost right' is the wordplay.
'local' becomes 'native' (relating to a particular area).
'banks' means one lot of letters goes inside another (bank can mean to surround or border).
'almost' means to remove the last letter (most of the word but not all of it).
'right' becomes 'r' (abbreviation).
'are' with its last letter taken away is 'ar'.
'ar'+'r'='arr'
'native' enclosing 'arr' is 'NARRATIVE'.
(Other definitions for narrative that I've seen before include "Report" , "Account of connected events, a story" , "Popeye's vegetable" , "Spoken account; story" , "Account describing events" .)