Closed with rite in unusual order, like monks in monastery (10)
I believe the answer is:
cloistered
'like monks in monastery' is the definition.
(monks are often found in cloisters)
'closed with rite in unusual order' is the wordplay.
'with' means one lot of letters go next to another.
'in unusual order' is an anagram indicator.
'closed'+'rite'='closedrite'
'closedrite' with letters rearranged gives 'CLOISTERED'.
(Other definitions for cloistered that I've seen before include "Being cut off from the world" , "with covered arcades" , "Sheltered from outside society" .)