Island origin of Cambridge university graduate (4)
I believe the answer is:
cuba
'island' is the definition.
(Cuba is an example)
'origin of cambridge university graduate' is the wordplay.
'origin of' says to take the initial letters.
'graduate' becomes 'ba'.
The first letters of 'cambridge university' is 'cu'.
'cu'+'ba'='CUBA'
(Other definitions for cuba that I've seen before include "Long rum-based drink" , "Caribbean nation" , "Castro's country" , "Caribbean country of cigars and rum?" , "Largest West Indies island" .)