Conservative branch to rise (5)

I believe the answer is:

climb

'to rise' is the definition.
(synonyms)

'conservative branch' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'branch' becomes 'limb' (I've seen this before).
'c'+'limb'='CLIMB'

(Other definitions for climb that I've seen before include "Ascend - ascent" , "Move upwards, ascend" , "Rise (in value, status)" , "Ascend, scale" , "Go higher up" .)

I've seen this clue in The Times and the Sydney Morning Herald.

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