Supports not starting dessert (6)
I believe the answer is:
afters
'dessert' is the definition.
(I've seen this before)
'supports not starting' is the wordplay.
'supports' becomes 'rafters' (rafter is a kind of support).
'not starting' means to remove the first letter.
'rafters' with its first letter taken away is 'AFTERS'.
(Other definitions for afters that I've seen before include "food for pudding" , "Pud" , "Dessert, sweet" , "Strafe with desserts" , "Informal desserts, puddings" .)