From J-Novel Club:
After her death on Earth, teacher Aoi Konominato awakens as a child in an unfamiliar world, filled with regret about her lackluster life and unfinished goals. An elven sage named Owain takes her in, mentors her, and instructs her in the art of sorcery. Twelve years later, Aoi has mastered everything he’s thrown at her, and Owain deems her ready to further her studies of sorcery by becoming an instructor at the illustrious Fiddich Academy, the finest sorcery school in the world. Though she’s hesitant at first, Aoi sees this as a second chance to become her ideal vision of a teacher, albeit in a fantasy world. However, this magical school is brimming with problems and misbehaving students. The children of nobles and royalty are used to doing whatever they want, but soon they’ll learn to pay attention in this fearsome witch’s class!