Make later improvements to crumbling outer surfaces of church (7)
I believe the answer is:
retouch
'make later improvements' is the definition.
'crumbling outer surfaces of church' is the wordplay.
'crumbling' indicates anagramming the letters.
'surfaces of' says to hollow out the word (remove centre letters).
'church' with its centre taken out is 'ch'.
'outer' is an anagram of 'retou'.
'retou'+'ch'='RETOUCH'
'to' is the link.
(Other definitions for retouch that I've seen before include "Fine-tune" , "Paint over" , "Correct painting" , "Improve a photo, with a pencil say" , "Make slight improvements to (a photo/picture)" .)