Supervise across diocese (7)
I believe the answer is:
oversee
'supervise' is the definition.
(I know that supervise can be written as oversee)
'across diocese' is the wordplay.
'across' becomes 'over' (synonyms).
'diocese' becomes 'see' (both can mean a cathedral area).
'over'+'see'='OVERSEE'
(Other definitions for oversee that I've seen before include "guide" , "Invigilate" , "Inspect" , "risk eyestrain?" , "Administer" .)