Foundation exists to support graduates (5)
I believe the answer is:
basis
'foundation' is the definition.
(I know that basis is a type of foundation)
'exists to support graduates' is the wordplay.
'exists' becomes 'is' (if something 'is', it exists).
'to support' is a charade indicator (letters next to each other) (in a down clue, some letters hold others up).
'graduates' becomes 'BAs' (people with Bachelor of Arts degrees).
'is' after 'bas' is 'BASIS'.
(Other definitions for basis that I've seen before include "Groundwork, foundation" , "Ground, foundation" , "First principle" , "Underlying support (for an idea)" , "grounds" .)