Stifle study covering a politician (6)
I believe the answer is:
dampen
'stifle' is the definition.
('dampen' can be a synonym of 'stifle')
'study covering a politician' is the wordplay.
'study' becomes 'den' (I've seen this before).
'covering' indicates putting letters inside.
'politician' becomes 'mp'.
'a'+'mp'='amp'
'den' enclosing 'amp' is 'DAMPEN'.
(Other definitions for dampen that I've seen before include "Make moist or depressed" , "get a bit wet" , "Stifle" , "Moisten" , "Make moist or depress spirit" .)