When you create an Advance Booking, there are 3 options for expiry: "No", "Cancel on expiry" and "Highlight on expiry".
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If you choose "Cancel on expiry", then the customer cannot pay after the expiry date – their link will show a page saying their booking has been cancelled. You can't adjust the expiry date once it has been cancelled, so you will need to create a new booking if the customer does want to pay.

If you choose "Highlight on expiry", the customer can still pay after the expiry date. The expiry date is just there to set a reminder date for you to manually chase bookings that have not been paid.

If you choose "No", the link will not expire. The customer has no time limit within which to pay (their link will still work whenever they decide to make the payment) and you will not receive any reminders to manually chase bookings that have not been paid.