Phlegmatic Conservative kept in check (6)
I believe the answer is:
placid
'phlegmatic' is the definition.
(I've seen this before)
'conservative kept in check' is the wordplay.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'kept in' means one lot of letters goes inside another.
'check' becomes 'plaid'.
'c' going into 'plaid' is 'PLACID'.
(Other definitions for placid that I've seen before include "Calm of nature" , "Unexcitable" , "Serene - unruffled" , "Calm, phlegmatic" , "Quiet and still" .)