Quieter part of distillery (7)
I believe the answer is:
stiller
'quieter' is the definition.
('still' can be a synonym of 'quiet')
'part of distillery' is the wordplay.
'part of' indicates a hidden word.
'STILLER' is hidden in the letters of 'distillery'.
(Other definitions for stiller that I've seen before include "Calmer" , "Trellis (anag)" , "Moving less" .)