Damage politician in one broadcast (6)
I believe the answer is:
impair
'damage' is the definition.
(impairing is a kind of damaging)
'politician in one broadcast' is the wordplay.
'politician' becomes 'MP' (Member of Parliament).
'in' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'broadcast' becomes 'air' (to air on TV).
'i'+'air'='iair'
'mp' going within 'iair' is 'IMPAIR'.
(Other definitions for impair that I've seen before include "Hobble" , "Hurt or handicap" , "blunt" , "'Mar, spoil (6)'" , "Hinder" .)