Supporter failing to finish a drink (3)
I believe the answer is:
tea
'drink' is the definition.
(tea is a drink)
'supporter failing to finish a' is the wordplay.
'supporter' becomes 'tee' (a golf tee acts as a support).
'failing to finish' means to remove the last letter.
'tee' with its final letter removed is 'te'.
'te'+'a'='TEA'
(Other definitions for tea that I've seen before include "Assam or Darjeeling, for example" , "Light afternoon meal" , "Evening meal - eat up" , "The cup that cheers but not inebriates" , "This towel is for drying dishes" .)