Game politician gets seat (4)
I believe the answer is:
rump
'seat' is the definition.
('rump' can be a synonym of 'seat')
'game politician' is the wordplay.
'game' becomes 'ru' (rugby union).
'politician' becomes 'mp'.
'ru'+'mp'='RUMP'
'gets' is the link.
(Other definitions for rump that I've seen before include "Animal's hind quarters" , "Depleted legislators" , "Seat" , "Hind part of body" , "Unimportant remnant" .)