Smelly pudding, eat! (10)
I believe the answer is:
aftershave
'smelly' is the definition.
(I have seen 'A smelly' mean 'aftershave' so perhaps 'smelly' could also mean 'aftershave')
'pudding eat' is the wordplay.
'pudding' becomes 'afters' (both can mean dessert).
'eat' becomes 'have' (I've seen this in another clue).
'afters'+'have'='AFTERSHAVE'
(Other definitions for aftershave that I've seen before include "A smelly" , "styptic lotion" , "alcohol to splash on, say" , "soothing application" , "I'm slapped on the face" .)