Nun wandering around diocese is not observed (6)
I believe the answer is:
unseen
'is not observed' is the definition.
(I've seen this before)
'nun wandering around diocese' is the wordplay.
'wandering' indicates anagramming the letters.
'around' is an insertion indicator.
'diocese' becomes 'see' (both can mean a cathedral area).
'nun' anagrammed gives 'unn'.
'unn' going around 'see' is 'UNSEEN'.
(Other definitions for unseen that I've seen before include "Hidden from view" , "not spotted" , "Invisable" , "not exercising pupils?" , "Unnoticed" .)