Having recovered the dragon egg back in Bolderfall, Kaia travelled to Quarrycrest because she heard an egg specialist lived in the town. You will find Kaia in the first area of the town, right in the middle of it. You will need either Ophilia or Primrose to complete this quest, so head to the tavern if you don’t have either in your active party. Once you do and have started this Side Story, travel to the upper area of the town and look for an older man in the northern end. He is behind the equipment shop, so use Guide/Allure on him and bring him back to Kaia to complete the quest.