Grew in volume during a bad-mannered broadcast (7)
I believe the answer is:
accrued
'grew in volume' is the definition.
'during a bad-mannered broadcast' is the wordplay.
'during' becomes 'acc' (I can't explain this - if you can you should believe this answer much more).
'a bad-mannered' becomes 'rude' (I've seen this before).
'broadcast' shows a homophone (sound like) (how the word might sound on the radio or TV).
'rude' is a homophone of 'rued'.
'acc'+'rued'='ACCRUED'
(Other definitions for accrued that I've seen before include "Once built-up" , "Accumulated over time" , "Grew or accumulated like interest" .)