A fine caterer arranged support, following operation (9)
I believe the answer is:
aftercare
'support following operation' is the definition.
(medical support after an operation)
'a fine caterer arranged' is the wordplay.
'fine' becomes 'f' (abbreviation).
'arranged' is an anagram indicator.
'caterer' anagrammed gives 'tercare'.
'a'+'f'+'tercare'='AFTERCARE'
(Other definitions for aftercare that I've seen before include "Follow-up support" , "Treatment following release" , "Support to customer following a purchase" .)