A bishop immersed in local history? (9)
I believe the answer is:
narrative
'history?' is the definition.
(thesaurus)
'a bishop immersed in local' is the wordplay.
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'immersed in' is an insertion indicator.
'local' becomes 'native' ('native' can be similar in meaning to 'local').
'a'+'rr'='arr'
'arr' going into 'native' is 'NARRATIVE'.
(Other definitions for narrative that I've seen before include "Verbal account" , "Telling a story" , "relation" , "Storyline" , "Account of connected events, a story" .)