Give up, when empty, some little cup (9)
I believe the answer is:
demitasse
'little cup' is the definition.
(small coffee cup)
'give up when empty some' is the wordplay.
'give up' becomes 'demit' (to demit is to resign a position).
'when' becomes 'as'.
'empty' means to remove the middle letters.
'some' with its middle taken out is 'se'.
'demit'+'as'+'se'='DEMITASSE'
(Other definitions for demitasse that I've seen before include "little cup" , "Small cup for black coffee" , "Coffee-cup" .)