Conservative unwilling to supply material (5)
I believe the answer is:
cloth
'material' is the definition.
(I know that material can be written as cloth)
'conservative unwilling' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'unwilling' becomes 'loth' (similar in meaning).
'c'+'loth'='CLOTH'
'to supply' is the link.
(Other definitions for cloth that I've seen before include "Fabric, textile" , "Textiles" , "Sails" , "The clergy" , "rag" .)