Deacon broadcast both sides of the short story (8)
I believe the answer is:
anecdote
'short story' is the definition.
(I've seen this before)
'deacon broadcast both sides of the' is the wordplay.
'broadcast' is an anagram indicator (letters scattered or cast around).
'both sides of' suggests removing the centre (only the letters on the sides remain).
'the' with its centre taken out is 'te'.
'deacon' with letters rearranged gives 'anecdo'.
'anecdo'+'te'='ANECDOTE'
(Other definitions for anecdote that I've seen before include "Short entertaining story" , "Brief tale" , "Neat code (anag.)" , "A short amusing story, probably true" , "Yarn" .)