Hi!
So there are a few options here.
One is to go ahead and customize the submission form templates to add a new timezone field (the basics of safely overriding templates in this manner are covered in our Themer’s Guide – so that’s a great starting point) and you would need some further code to “catch” this extra data and store it.
I’m afraid that’s a tad more involved than we can help with – but you might also be interested in using Events Calendar PRO for this task. It provides additional fields that Community Events can also work with and you might for instance create a custom timezone field as a dropdown or set of radio inputs to let submitters provide their timezone.
Does that help here?