Building material firm, new, supported by Greek island (8)
I believe the answer is:
concrete
'building material' is the definition.
(concrete is a kind of building material)
'firm new supported by greek island' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'new' becomes 'n'.
'supported by' means one lot of letters go next to another (letters go below - in down clue).
'greek island' becomes 'crete' (I've seen this before).
'co'+'n'+'crete'='CONCRETE'
(Other definitions for concrete that I've seen before include "It's composed of sand, cement and water" , "Substantial, real" , "Unsightly building material" , "Building material - tangible" , "Not abstract or imaginary" .)