Commercial broadcast idiot put before new supplement (8)
I believe the answer is:
addition
'supplement' is the definition.
(thesaurus)
'commercial broadcast idiot put before new' is the wordplay.
'commercial' becomes 'ad'.
'broadcast' indicates anagramming the letters.
'put before' means one lot of letters go next to another.
'new' becomes 'n'.
'idiot' with letters rearranged gives 'ditio'.
'ad'+'ditio'+'n'='ADDITION'
(Other definitions for addition that I've seen before include "Reckoning" , "Annexe" , "Something extra" , "'Increase, augmentation (8)'" , "Calculation of the sum of numbers" .)