Conservative member to reach a higher position (5)
I believe the answer is:
climb
'to reach a higher position' is the definition.
'conservative member' is the wordplay.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'member' becomes 'limb' (limb is a kind of member**).
'c'+'limb'='CLIMB'
(Other definitions for climb that I've seen before include "Walk up" , "Scale or clamber" , "Go up - scale" , "Rise (in value, status)" , "improve one's social status" .)