Possibly shines a coarse fabric (7)
I believe the answer is:
hessian
'coarse fabric' is the definition.
(I've seen this before)
'possibly shines a' is the wordplay.
'possibly' indicates anagramming the letters.
'shines'+'a'='shinesa'
'shinesa' anagrammed gives 'HESSIAN'.
(Other definitions for hessian that I've seen before include "sackcloth?" , "Cloth for sacking" , "It's rather like sacking" , "Hemp, jute fabric" , "Coarse jute fabric" .)