Short story being broadcast, one that grips (5)
I believe the answer is:
talon
'one that grips' is the definition.
(I've seen this before)
'short story being broadcast' is the wordplay.
'short' means to remove the last letter.
'story' becomes 'tale' (synonyms).
'being broadcast' becomes 'on' (ie on TV or the radio).
'tale' with its last letter removed is 'tal'.
'tal'+'on'='TALON'
(Other definitions for talon that I've seen before include "The stock" , "Tonal (anag.)" , "part to make savage cuts" , "ogee moulding" , "Part of hobby" .)