Bishop accepting first female objective becoming minister (8)
I believe the answer is:
reverend
'minister' is the definition.
(I've seen this before)
'bishop accepting first female objective' is the wordplay.
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'accepting' indicates putting letters inside.
'first female' becomes 'eve' (adam and eve).
'objective' becomes 'end' (I've seen this before).
'rr' going around 'eve' is 'rever'.
'rever'+'end'='REVEREND'
'becoming' is the link.
(Other definitions for reverend that I've seen before include "Cleric's title" , "Clergyman's title" , "Priest's title" , "Minister" , "like Father Brown" .)