Conservative member punching chair person high on face? (4,7)
I believe the answer is:
rock climber
'person high on face?' is the definition.
(someone climbing a rock face)
'conservative member punching chair' is the wordplay.
'conservative member' becomes 'climb' (I can't explain this - if you can you should believe this answer much more).
'punching' indicates putting letters inside (some letters punch a hole in others).
'chair' becomes 'rocker' (rocker is a kind of chair).
'climb' placed into 'rocker' is 'ROCK-CLIMBER'.
(Another definition for rock climber that I've seen is " Outdoor type".)