Karisome Chouhi no Pride: Kouguu ni Saku Hana wa Mirai wo Koinegau

Via, the fourth princess, was impatient as the royal palace was busy fighting for succession. That's because the lewd emperor implied that he wanted her to be his concubine. Via lived unobtrusively in a sickly setup, but even as she stays still, things just get worse. Therefore, she decided to offer a time-limited concubine contract to the next emperor, the first prince, Alex. This is the story of the life of the unconventional Princess Via! (Source: Ichijinsha, translated)