Nun wandering around diocese is not observed (6)
I believe the answer is:
unseen
'is not observed' is the definition.
(I've seen this in another clue)
'nun wandering around diocese' is the wordplay.
'wandering' indicates anagramming the letters.
'around' indicates putting letters inside.
'diocese' becomes 'see' (I've seen this in another clue).
'nun' is an anagram of '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" .)