Kate is investigating a magical being who has apparently become a Mary. Similar to Typhoid Mary, this is a person who has been infected and spread the virus. This investigation gets difficult, and is not made easier by the tension between her and the Beast Lord, and is further complicated by her employment by the Order.
The battles in the tournament are something else. In them, we learn something about Kate, and she is forced to do something and risk giving away her past which she is trying to keep secret. She is worried about how others will react to this piece of her past. I'm not going to say what it is, because, spoiler. You'll just have to read the book to find out.