Maybe Korra travels back in time and meets the first Avatar. This encounter could lead to her learning ancient bending techniques directly from the source. She might also get involved in the political and social issues of that era, and her modern - day ideas could cause a stir. She could try to change the way the Avatar was perceived in the past, which would then have a ripple effect on her own time.
One possible plot could be Korra going back in time to prevent a great disaster that she has knowledge of in her own time. For example, she might go back to stop the start of a war that had long - lasting negative impacts on the world. She could use her bending skills in new and unexpected ways in the past, as the technology and bending styles of that time might be different.
In a 'Korra travels back in time fanfiction', it could be that Korra goes back to a time when bending was just emerging. She has to hide her advanced bending abilities at first. She then starts to teach the early benders some of the more refined forms she knows. This changes the course of bending history, and when she returns to her own time, she finds that bending has evolved in a completely different way.