Possibly, as Hamlet put it, to dream? (9)
I believe the answer is:
perchance
'possibly' is the definition.
(synonyms)
'hamlet put it to dream?' is the wordplay.
I cannot really see how this works, but
'put' could be 'per' and 'per' is found within the answer.
'it' could be 'e' ('e' can mean 'electronic' which is similar to 'IT') and 'e' is present in the answer.
This may be the basis of the clue (or it may be nonsense).
'as' acts as a link.
Can you help me to learn more?
(Other definitions for perchance that I've seen before include "As it may happen" , "possibly" , "'To sleep: -------- to dream:' Hamlet" , "Maybe (to dream? - Hamlet)" .)