Conservative, flexible in support of party, is an upstart (6,7)
I believe the answer is:
social climber
'an upstart' is the definition.
(social climber is a kind of upstart)
'conservative flexible in support of party' is the wordplay.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'flexible' becomes 'limber' ('limber' can be similar in meaning to 'flexible').
'in support of' is a charade indicator (letters next to each other) (I've seen this in other clues).
'party' becomes 'social' (social is a kind of party**).
'c'+'limber'='climber'
'climber' put after 'social' is 'SOCIAL CLIMBER'.
'is' is the link.
(Other definitions for social climber that I've seen before include "One aiming for higher status" , "One seeking higher status" , "Parvenu" , "Someone wanting higher status" , "status-seeker?" .)