Waste processing centre's smell not entirely healthy (5)
I believe the answer is:
bowel
'waste processing centre's' is the definition.
'smell not entirely healthy' is the wordplay.
'smell' becomes 'bo' (abbreviation for Body Odour).
'not entirely' means to remove the last letter.
'healthy' becomes 'well' ('well' can be similar in meaning to 'healthy').
'well' with its final letter taken off is 'wel'.
'bo'+'wel'='BOWEL'
(Other definitions for bowel that I've seen before include "Gut" , "Large intestine" , "part of canal" .)