Sweeter sort of broadcast? (6)
I believe the answer is:
kinder
'sweeter' is the definition.
'sort of broadcast?' is the wordplay.
'sort of' becomes 'kinda' (informal way of saying 'kind of').
'broadcast?' shows a homophone (sound like) (how the word might sound on the radio or TV).
'kinda' sounds like 'KINDER'.
(Other definitions for kinder that I've seen before include "More agreeable" , "Scout may follow this" , "with less severity" , "more pleasant" , "More considerate and helpful" .)