TPE sell Airport Advance tickets for journeys from Manchester Airport, which allow you to take a later TPE service on certification of your delay at the ticket office, if your booked train is at least an hour after your flight's scheduled arrival time.
Unfortunately Northern don't sell Airport Advances, so you buy normal Advances from at your own risk in case your flight is delayed. You can of course change Advance tickets to a different date/time (or change them to a walkup ticket) but this needs to be done/requested before the scheduled train departure time. So you would either have to do it at your origin airport if you can see your flight is being delayed too much to make your train, or during the flight if you have access to inflight WiFi.
Personally speaking I choose to take the risk by buying Northern Advances, changing them to a later train where necessary. However I only do this because I am familiar with the process (having been delayed arriving into Manchester Airport lots of times!) and fly with airlines that offer WiFi.