Games of Flame and Dust by Val Saintcrowe

Fourth Wing but edgier.

Banyan Thriceborn has always been different, but it’s never been a good thing. Until now.

When she competes in a tournament for admission to the South Ridge Dragon Academy, she gets noticed by Odion Naxim. Odion is the most promising student at the Academy, brilliant and daring, the best hope the Trinal Kingdoms has to banish the menace of the Frost.
Odion sees Banyan’s potential as a soldier. And he wants her.
Before Banyan knows it, she’s enrolled as a student at the Academy. The curriculum mostly consists of wargames—battles in an arena, students soaring on gliders, pelting each other midflight with blunt arrows.
Banyan wins all the games, but being the best doesn’t endear her to the other students. Neither does being the purported object of Odion’s desire. His heated gaze follows her through the halls of the school, even as he does nothing to pursue her.
There are whispers Banyan is meant to bond the dragon mated to Odion’s, that they will be a bonded pair who will lead the fight against the Frost.
But for now, he is her rival, the only student she struggles to defeat in the arena.
All the while, the Frost is lurking out on the reaches of Ice Mountains, in the frozen peaks, waiting to strike.