Mother didn’t finish the tea (4)
I believe the answer is:
mate
'the tea' is the definition.
(South American hot drink)
'mother didn't finish' is the wordplay.
'mother' becomes 'mater' (old-fashioned term for mother).
'didn't finish' means to remove the last letter.
'mater' with its last letter taken away is 'MATE'.
(Other definitions for mate that I've seen before include "provides solution to chess problem" , "Friend; chess ending" , "Team (anag.)" , "Friend, partner" , "Team up with partner" .)