Possibly sit on cane construction (9)
I believe the answer is:
perchance
'possibly' is the definition.
(synonyms)
'sit on cane construction' is the wordplay.
'sit' becomes 'perch' (perching is a kind of sitting).
'on' indicates putting letters inside.
'construction' indicates anagramming the letters (answer constructed from certain letters).
'cane' with letters rearranged gives 'ance'.
'perch' inserted inside 'ance' is 'PERCHANCE'.
(Other definitions for perchance that I've seen before include "possibly" , "'To sleep: -------- to dream:' Hamlet" , "As it may happen" , "Maybe (to dream? - Hamlet)" .)