Do the characters end when the abyss league ends?

Hi Im a new player. Im currently level 60odd on my first build and loving it.

My question is that when the abyss league ends do our characters go or can we use then in the new league?

At the end of a league, your current league characters & stash contents get transferred to Standard where you can continue to use them... though not many do. They aren't available in the next league, no. That's a completely fresh start.