How do you battle a trainer in the great league?

I am worried that this is going to involve another human having to help. For the jump start research tasks I need to battle another trainer in the great league.

I am level 31 and I’ve no idea what the great league is. I have had a look around the games menu and I can’t find anything that would suggest what it is either.

How do I find the great league and how do I battle other trainers. Is it possible to complete this task without needing to coordinate it with another person? Can I just battle some random person online?