Story's thread (4)
I believe the answer is:
yarn
This clue is a double definition.
'story's' is the first definition.
(synonyms)
'thread' is the second definition.
(synonyms)
(Other definitions for yarn that I've seen before include "Long involved story" , "that'll keep you in stitches?" , "Rambling tale" , "Spun thread or wool or tall tale" , "Exaggerated story or spun thread" .)