So, for this plot, it would take place after Amon stole Korra's bending. For this storyline, she would have forced Amon into retreat, and he would go out like he had in the series. Except Korra would have only her Air bending. She would have relied on her friends in order to do this monumental feat. Afterwards, during the peace she would spend a year mastering Air. This would make her 18. From here, she would get visited by Aang, who would tell Korra that she must find and learn her bending from specific teachers. And that she had must start with the most opposite element to Air, Earth. Not being given any instruction as to who her masters must be, she has no idea she is going to meet the man who would teach her Earth bending once again.
The chance encounter would happen when Korra is ambushed by firearm wielding Triad punks. The new technology hailing from the Western civilization has managed to give non-benders a chance against benders. It allows them to shoot out non-bendable projectiles at such speed that not even air, nor ice can stop it. A powerful enough Air bender could redirect the bullet, however if in sustained fire would find it difficult to do so. The gun wielding perpetrators would push her into an alley, and try to take her hostage. This is when her master would arrive, he a bender who traveled with is father to the West, had his father taken from him in the start of the gun trade. Benders' were even LESS common in the West than anywhere else, and they were highly feared and looked down upon, and so his father was killed protecting innocents. From then on, Desmon had trained in secret in order to be able to perform the highly effective gun. As well as outwit the wielder. From their fated encounter, Desmon would take up Korra as his apprentice and take her back West with him. There she would learn to master Earth bending, in the way that would be best for her. Pure, live, and real combat, watching it and partaking in it.
From here, we could even move on to potential other Masters, I wouldn't mind going as far as doing all 3 elements going in order of Earth, Water, Fire. If anyone is interested in doing this with me. I'd love to get it going sometime soonish. PM me if you're interested!