Unwilling to follow Conservative ministers? (5)
I believe the answer is:
cloth
'ministers?' is the definition.
(I've seen this before)
'unwilling to follow conservative' is the wordplay.
'unwilling' becomes 'loth' (similar in meaning).
'to follow' says to put letters next to each other (some letters go after or follow others).
'conservative' becomes 'C' (UK political abbreviation).
'loth' put after 'c' is 'CLOTH'.
(Other definitions for cloth that I've seen before include "Woven material" , "The clergy" , "Gingham, say" , "rag" , "Textiles" .)