Part of this secret noise of contempt (4)
I believe the answer is:
hiss
'noise of contempt' is the definition.
'part of this secret' is the wordplay.
'part of' indicates a hidden word.
'HISS' is hidden within 'this secret'.
(Other definitions for hiss that I've seen before include "Make disapproving sound" , "showing contempt?" , "Make sibilant sound of disapproval as at villain" , "Jeer" , "Urgent whisper" .)