Heartless rubbish broadcast through arrogance (6)
I believe the answer is:
hubris
'arrogance' is the definition.
(I know that hubris is a type of arrogance)
'heartless rubbish broadcast' is the wordplay.
'heartless' means to remove the middle letters.
'broadcast' indicates anagramming the letters (letters scattered or cast around).
'rubbish' with its centre removed is 'rubish'.
'rubish' with letters rearranged gives 'HUBRIS'.
'through' is the link.
(Other definitions for hubris that I've seen before include "The pride that goeth before a fall" , "Arogant pride and egotism" , "Arrogance or over-confidence" , "feeling of superiority" , "The pride that goes before a fall" .)