Broadcast a silly scare about a race (7)
I believe the answer is:
scatter
'broadcast' is the definition.
(I've seen this before)
'a silly scare about a race' is the wordplay.
'a silly' is an anagram indicator.
'about' is an insertion indicator.
'a race' becomes 'tt'.
'scare' anagrammed gives 'scaer'.
'scaer' enclosing 'tt' is 'SCATTER'.
(Other definitions for scatter that I've seen before include "Separate and move off in different directions" , "Disperse, thrown around" , "Dissipate" , "Throw randomly" , "Sprinkle" .)