Conservative party member demanding vessel (9)
I believe the answer is:
hardliner
'conservative party member' is the definition.
'demanding vessel' is the wordplay.
'demanding' becomes 'hard' ('hard' can be similar in meaning to 'demanding').
'vessel' becomes 'liner' (liner is a kind of vessel**).
'hard'+'liner'='HARDLINER'
(Other definitions for hardliner that I've seen before include "One committed to an uncompromising policy" , "One's rigorous in application" , "Uncompromising advocate" , "Doctrinaire type" , "man of principle" .)