During his attempts to summon Chole O'Bell, Leon accidentally summoned Shizue. To keep her body from collapsing, he let the Flame Giant Ifrit possess her.
Shizue thought of Yuuki as a reliable student. She's proud of him gaining the position of Grand Master.
Yuuki was the one who taught Shizue about video games, and specifically the quote: "I'm not a bad slime, you know."
Shizue often worries about her student Hinata, although she's very capable Hinata is the type to shoulder all the world's darkness within her. Because Shizue believes in Hinata, she chose to support Yuuki over Hinata.
Under the short time they were together they became good friends. Due to both of them originally coming from Japan their relationship grew quickly.