Support has left a taste (7)
I believe the answer is:
flavour
'a taste' is the definition.
(I know that flavour is a type of taste)
'support has left' is the wordplay.
I cannot really see how this works, but
'left' could be 'l' (common abbreviation) and 'l' is found within the answer.
'support' could be 'favour' (I've seen this before) and 'favour' is found in the remaining letters.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for flavour that I've seen before include "Characteristic quality of something" , "Distinctive taste" , "essential quality" , "Relish" , "Season" .)