All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
It is absolutely impermissible to pray the Thuhr before its time begins. Since the plane will land before the ‘Asr prayer, then you have to pray the Thuhr at the airport because its time will not have expired yet.
You may pray it combined and shortened with the ‘Asr, either in advance (within the time of the Thuhr) or delayed (within the time of the ‘Asr), if you are too busy with travel procedures and the airport is outside the town which you are heading to, because your travel (trip) is not over yet, so you are entitled to take the concessions of traveling, and this only ends when you enter your hometown.
If the airport is inside the town which you are heading to, however, then you have to pray them in their complete form, without shortening them, as you are not entitled to shorten them. In this case, your belief that you are not permitted to combine between the Thuhr and the ‘Asr – after arriving at your hometown – is correct, because combining prayers is among the concessions of traveling, and your trip will end by your arrival at your hometown.
You are permitted to pray the Thuhr in the plane and shorten it if you are able to fulfill its standing, bowing, and so on, but if you are not able to do so, then you should delay the prayer until you arrive at the airport so that you are able to pray correctly, and you combine it with the ‘Asr prayer if the airport is outside your hometown – as we have already stated – as long as you do not fear that its time will expire.
The fatwa of Ibn ‘Uthaymeen reads, “If the plane lands before the expiry of the time of the present prayer, or the prayer which comes next, and if these are two prayers that can be combined together, then one should not pray in the plane because one is unable to fulfill what must be fulfilled [regarding the obligations of the prayer], so one has to delay the prayer until their arrival and then pray it on land so that they are able to fulfill its obligations.”
Allah knows best.