If you don't want to cancel a booking and then create a new one, you can just edit the current one as long as it is the same activity.
1. Go to Activities overview and find the activity you want to edit.
2. After you click on the activity, scroll down to the Info attendees section. Click on the 3 dots of the booking you want to edit and then Edit booking.
3. On the Date and time section, choose the new schedule for that booking and click on Update.
4. Done, your client will be informed of the changes.