Edward rejected the last of smelly refuse (4)
I believe the answer is:
deny
'refuse' is the definition.
(I know that deny is a more specific form of keep back)
'edward rejected the last of smelly' is the wordplay.
'edward' becomes 'Ned'.
'rejected' shows that the letters should be reversed in order.
'the last of' suggests the final letters.
The last letter of 'smelly' is 'y'.
'ned' in reverse letter order is 'den'.
'den'+'y'='DENY'
(Other definitions for deny that I've seen before include "Refuse; repudiate" , "Gainsay" , "Refuse to admit (something)" , "Reject as true" , "Controvert" .)