Foundation established by graduates coming to island (5)
I believe the answer is:
basis
'foundation' is the definition.
(I know that foundation can be written as basis)
'graduates coming to island' is the wordplay.
'graduates' becomes 'BAs' (people with Bachelor of Arts degrees).
'coming to' is a charade indicator (letters next to each other).
'island' becomes 'is' (abbreviation).
'bas'+'is'='BASIS'
'established by' is the link.
(Other definitions for basis that I've seen before include "Form of support" , "Principal element" , "grounds" , "Fundamental part" , "First principle" .)