Spoil Independent politician's broadcast (6)
I believe the answer is:
impair
'spoil' is the definition.
('impair' can be a synonym of 'spoil')
'independent politician's broadcast' is the wordplay.
'independent' becomes 'i'.
'politician' becomes 'mp'.
'broadcast' becomes 'air' ('air' can be a synonym of 'broadcast').
'i'+'mp'+'air'='IMPAIR'
(Other definitions for impair that I've seen before include "'Mar, spoil (6)'" , "Courteous man (colloq.)" , "Make worse or less effective" , "blunt" , "Harm" .)