Look after complete bishopric (7)
I believe the answer is:
oversee
'look after' is the definition.
'complete bishopric' is the wordplay.
'complete' becomes 'over' (I've seen this in other clues).
'bishopric' becomes 'see' (I've seen this before).
'over'+'see'='OVERSEE'
(Other definitions for oversee that I've seen before include "guide" , "survey" , "Inspect" , "Supervise, keep an eye on" , "Supervise like ganger" .)