Complimentary broadcast drops independence (4,4)
I believe the answer is:
free rein
'independence' is the definition.
(I've seen this in another clue)
'complimentary broadcast drops' is the wordplay.
'complimentary' becomes 'free' (synonyms).
'broadcast' shows a homophone (sound like) (how the word might sound on the radio or TV).
'drops' becomes 'rain' (drops of water).
'rain' sounds like 'rein'.
'free'+'rein'='FREE REIN'
(Other definitions for free rein that I've seen before include "Give it to remove all constraints" , "Unlimited scope for action" , "'The removal of constraints (4,4)'" , "Carte blanche" , "Liberty over actions" .)