Follow a story that's heard (4)
I believe the answer is:
tail
'follow' is the definition.
(both can mean to chase or pursue)
'a story that's heard' is the wordplay.
'a story' becomes 'tale' ('tale' can be a synonym of 'story').
'that's heard' shows a homophone (sound like).
'tale' sounds like 'TAIL'.
(Other definitions for tail that I've seen before include "Follow -- rear end" , "Shadow" , "part of coat" , "Elongated posterior part of an animal" , "Follow (a suspect)" .)