Waste could be dormouse's occasionally (5)
I believe the answer is:
dross
'waste' is the definition.
(I know that dross is a type of waste)
'dormouse's occasionally' is the wordplay.
'occasionally' means one should take alternating letters (letters taken at regular intervals or occasions).
The alternating letters of 'dormouses' are 'DROSS'.
'could be' is the link.
(Other definitions for dross that I've seen before include "of no value" , "Refuse - dregs" , "Waste matter, refuse" , "Worthless matter" , "Lees" .)