New webinar dates (Recurring)

Yes, you'll have to edit All existing Webinars and extend the dates and confirm you have selected Attendees register once and can attend any of the occurrences

... and to add to what @Lennie said above, make sure you do it before the last day of your current webinar setup; otherwise, that Webinar ID will expire and there's no way to retrieve and use it once that happens (you'd have to make a new session).