Material found in Welsh river by Greek character (7)
I believe the answer is:
taffeta
'material' is the definition.
(taffeta is a kind of material)
'welsh river by greek character' is the wordplay.
'welsh river' becomes 'taff' (I've seen this before).
'by' says to put letters next to each other.
'greek character' becomes 'eta' (letter from the Greek alphabet).
'taff'+'eta'='TAFFETA'
'found in' acts as a link.
(Other definitions for taffeta that I've seen before include "Crisp, smooth, lustrous fabric" , "Thin crisp lustrous silk" , "Lustrous silky fabric" , "Fine crisp silk fabric" , "Fabric - fat fate (anag)" .)