Costlier renovation for monastery, say? (8)
I believe the answer is:
cloister
'monastery say?' is the definition.
(monastery is a kind of cloister)
'costlier renovation' is the wordplay.
'renovation' indicates an anagram.
'costlier' with letters rearranged gives 'CLOISTER'.
'for' acts as a link.
(Other definitions for cloister that I've seen before include "ambulatory" , "Cathedral court walkway" , "Place of religious retreat" , "Covered walkway in religious establishment" , "put within walls" .)