Erect building on Greek island (5)
I believe the answer is:
crete
'greek island' is the definition.
(Crete is a Greek island)
'erect building' is the wordplay.
'building' indicates anagramming the letters.
'erect' anagrammed gives 'CRETE'.
'on' is the link.
(Other definitions for crete that I've seen before include "Major island south of Greece" , "Large Greek island" , "Large Mediterranean island" , "Knossos island" , "Mediterranean island with Minoan remains" .)