English bishop and mission (6)
I believe the answer is:
errand
'mission' is the definition.
(thesaurus)
'english bishop and' is the wordplay.
'english' becomes 'e' (abbreviation).
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'e'+'rr'+'and'='ERRAND'
(Other definitions for errand that I've seen before include "In purposeful trip" , "Journey to deliver message etc" , "short shopping trip" , "Mission (usually run!)" , "Commission, task" .)