A Princess in the Underworld

On a planet with only two inhabited continents, a queen had to choose which one of her triplet daughters would succeed her. As queen, it was her duty to kill the other two princesses to ensure the new queen would not have any rivals with a claim to the throne. Instead of killing the other two princesses, she sent them on dangerous missions, hoping they would never return. Eisla's mission was to bring law and order to an underground city where women often fought each other to the death.
The princess had to survive in the underworld for a year before she could return.  However, even if she could survive the underground arena, Eisla would still have to convince her mother she would be the best choice to succeed her, or she would have to fight for her life in the arena.