A composition finally being broadcast soon (4)
I believe the answer is:
anon
'soon' is the definition.
(synonyms)
'a composition finally being broadcast' is the wordplay.
'finally' indicates one should take the final letters.
'being broadcast' becomes 'on' (ie on TV or the radio).
The last letter of 'composition' is 'n'.
'a'+'n'+'on'='ANON'
(Other definitions for anon that I've seen before include "In the near future" , "Soon, in a little while" , "Soon - unknown author (abbr)" , "Having no known name" , "Soon; unnamed" .)