Not commencing old story (4)
I believe the answer is:
tale
'story' is the definition.
(synonyms)
'not commencing old' is the wordplay.
'not commencing' means to remove the first letter.
'old' becomes 'stale' (synonyms).
'stale' with its first letter removed is 'TALE'.
(Other definitions for tale that I've seen before include "Late with a story" , "Report" , "Anecdotal narrative" , "Story or anecdote" , "Old wives' recital?" .)