Dog story heard (4)
I believe the answer is:
tail
'dog' is the definition.
('tail' can be a synonym of 'dog')
'story heard' is the wordplay.
'story' becomes 'tale' ('tale' can be a synonym of 'story').
'heard' indicates a 'sounds like' (homophone) clue.
'tale' sounds like 'TAIL'.
(Other definitions for tail that I've seen before include "Trail (behind comet)" , "Dog - or part of one" , "Follow; end part" , "Private investigator" , "Shadow" .)