Chimney went skyward, we're told (4)
I believe the answer is:
flue
'chimney' is the definition.
(thesaurus)
'went skyward we're told' is the wordplay.
'went skyward' becomes 'flew'.
'we're told' indicates a 'sounds like' (homophone) clue.
'flew' sounds like 'FLUE'.
(Other definitions for flue that I've seen before include "Chimney-shaft" , "Hot air it conveys" , "smoky passage" , "Escape" , "Fume vent" .)