Man blowing top, Greek character delivering material (7)
I believe the answer is:
taffeta
'material' is the definition.
(taffeta is a kind of material)
'man blowing top greek character' is the wordplay.
'man' becomes 'staff' (both can mean to work at a particular post).
'blowing top' means to remove the first letter.
'greek character' becomes 'eta' (letter from the Greek alphabet).
'staff' with its first letter taken off is 'taff'.
'taff'+'eta'='TAFFETA'
'delivering' is the link.
(Other definitions for taffeta that I've seen before include "Sheeny fabric" , "Fine crisp lustrous fabric" , "Glossy silk material" , "Fabric - fat fate (anag)" , "fine stuff indeed!" .)