Rise of conservative member (5)
I believe the answer is:
climb
'rise' is the definition.
(I know that rise can be written as climb)
'conservative member' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'member' becomes 'limb' (member can mean a limb).
'c'+'limb'='CLIMB'
'of' acts as a link.
(Other definitions for climb that I've seen before include "What mountaineer does" , "Get a rise" , "Deadened" , "Go higher up" , "Soar" .)