She is the fighter of the female Zero pair.
Until they met, both pairs believed they were the only Zero pair to exist. Both teams are experiments created by Nagisa at different times, and the female pair is presumably the first generation. Despite their unusual background, both Kouya and Yamato attend high school, although different ones.
Kouya, unlike Yamato, is very serious and does not take things lightly. She is reserved though Yamato is the only one who is able to get her to open up.
She meets Yamato when they are both young and were trained together to work as the Zero pair. While growing up, her feelings for Yamato grew stronger until both girls had fallen in love with one another.
She is deeply in love with Yamato despite trying to hide it from others. Her cold, aloof exterior is armour for her true feelings; she is truly afraid that she will lose Yamato. It gets to the point that she even ends up throwing up from fear at the idea of being separated from her lover and pair.
It is more than evident that Kouya has had sex with Yamato, as both girls clearly have a physical and romantic relationship alongside their professional relationship as Zero. In an interesting demonstration of the series' fictional world's rules and expectations of society, Kouya wears fake cat ears despite not being a virgin. Yamato often teases her about it, particularly because Yamato doesn't try to hide her status.