That still leaves shady(I suspect it's supposed to be the player's future self trapped in the past and there is a quest revolving around shady obtaining the four elements/plus I think it'd be kinda cool), Tenzin's son, or korra(I hope not), if going by the you can only learn the bending your body is capable of pattern...
BUT, there is precedent for being taught by the spirits/past lives in spirit form(not limited to the body's capabilities) and just not really needing to actually use airbending, so it could just be anyone including her teammates who given that Tenzin trains the team subplot could also pick stuff up there. If they end up skipping forward in time to when random people get airbending though they can just make a new character like what happened in book 2.