Building material for start of construction on Greek island (8)
I believe the answer is:
concrete
'building material' is the definition.
(concrete is a kind of building material)
'start of construction on greek island' is the wordplay.
'start of' suggests taking the first letters.
'greek island' becomes 'crete' (Crete is a Greek island).
The first letter of 'construction' is 'c'.
'c'+'on'+'crete'='CONCRETE'
'for' is the link.
(Other definitions for concrete that I've seen before include "setter" , "Real; building material" , "Substantial, real" , "Firm" , "Real, not abstract" .)