The Time Tournament by Lara Bronson

Elena
Time-traveling witches, dragon lairs, a world pulled straight out of a fantasy. Except, this became my life overnight, and I had no idea how to handle it. One minute, I was walking through European woods with my family. Next, I was thrown into a realm beyond my wildest dreams. Danger lurked around every corner, and the only one willing to help was the lord of the Crimson Dragon House.
Then I met his son, Killian. Words can’t even begin to describe how much I despise him. Arrogance runs through his veins as strongly as my hatred runs through mine. When I became a dragon rider, I was about to face grueling challenges and Killian was determined to make me fail. With no way back to my own time, my only shot at survival was to master dragon riding and Killian won’t stand in my way. I just have to figure out how.

Killian
She ended up in my lair by accident, but her very presence makes my blood boil. My father’s decision to welcome her into Moltenclaw Keep and let her train as a rider was beyond me. The old man must’ve lost his marbles.
On top of dealing with my mother’s death, now I have to train this weak human girl who can barely hold a sword. And if that wasn’t bad enough, soon the Hungarian king will summon us and four other dragon houses for the Time Tournament.
But no matter what, one thing is certain. I’m going to drive that girl out of my lair, my life, and my mind.