Relinquish valuable item, mostly for drink (9)
I believe the answer is:
demitasse
'drink' is the definition.
(demitasse is a kind of drink)
'relinquish valuable item mostly' is the wordplay.
'relinquish' becomes 'demit' (I've seen this in another clue).
'valuable item' becomes 'asset' (an asset is something valuable or advantageous).
'mostly' means to remove the last letter (most but not all of the word).
'asset' with its final letter removed is 'asse'.
'demit'+'asse'='DEMITASSE'
'for' acts as a link.
(Other definitions for demitasse that I've seen before include "Small cup for black coffee" , "little cup" , "Coffee-cup" .)