Tea man hasn't finished (3)
I believe the answer is:
cha
'tea' is the definition.
(cha is a type of tea)
'man hasn't finished' is the wordplay.
'man' becomes 'chap' (I've seen this in other clues).
'hasn't finished' means to remove the last letter.
'chap' with its last letter taken off is 'CHA'.
(Other definitions for cha that I've seen before include "Tea (colloq.)" , "Rosie Lee (slang)" , "Tea (informal)" , "not allowed in ski lodge" , "drink" .)