So, you know how Aang is the last airbender in existence, and there won't be anyone to teach any future Avatars airbending?

Well, there are two ways I can think of to get around that.

First Method

Assuming Katara and Aang have kids when they grow up, their kids' genes will be half airbender, half waterbender. Now since there's no such thing as someone who can bend two elements, that means they have a chance of producing airbenders as well as waterbenders. Their airbending children can learn from their father (Aang) and go on to marry other people from other nations, also having a chance of producing airbending children. By the time Aang dies, there will be enough airbenders to teach the next Avatar how to airbend.

Or, if that does not seem plausible to you, or if you don't support Kataang, there is another way it could happen.

Second Method

Remember how each bending art was learned from a different nonhuman thing?

Airbending = Sky Bison

Waterbending = The Moon

Firebending = Dragons

Earthbending = Badgermoles

The first human benders taught themselves to bend by studying these sources. Theoretically, this also means that almost anybody can learn to bend. So, Aang could give airbending lessons to nonbenders of other countries by lending them Appa. Eventually, airbending will be a common bending art once again, so even after Aang's death, there will be airbenders to teach future Avatars.

Does this make sense to any of you?