From Manga UP:
Sylph Biebel, the duke's daughter, has just suffered a sinister plot by a friend, resulting in her engagement to the prince being called off and her own banishment. But she's not just sent anywhere. She gets exiled to a kingdom where an infamous monster resides. Will her quick wit win this king's favor as she begins a new life as a librarian in a mysterious land?

https://www.cmoa.jp/title/243182/