Increases in Conservative branches (6)
I believe the answer is:
climbs
'increases' is the definition.
(climbing is a kind of increasing)
'conservative branches' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'branches' becomes 'limbs' (I've seen this in another clue).
'c'+'limbs'='CLIMBS'
'in' is the link.
(Other definitions for climbs that I've seen before include "Moves upwards" , "Ascends with difficulty" , "Moves upward gradually" , "Advances" , "Ascends a hill or ladder" .)