Lack of faith shown by Delibes, I suspect, before start of fugue (9)
I believe the answer is:
disbelief
'lack of faith' is the definition.
(I've seen this before)
'delibes i suspect before start of fugue' is the wordplay.
'suspect' indicates an anagram.
'before' is a charade indicator (letters next to each other).
'start of' indicates taking the first letters.
The first letter of 'fugue' is 'f'.
'delibes'+'i'='delibesi'
'delibesi' is an anagram of 'disbelie'.
'disbelie'+'f'='DISBELIEF'
'shown by' is the link.
(Other definitions for disbelief that I've seen before include "Incredulity" , "Lack of faith" , "Refusal to advance credit" , "having exhausted trust fund?" .)