A member of the ranking nobility of her native planet Elas, which was at war with the planet Troyius. Elaan carried the title of Dohlman. In 2268 she was betrothed to the leader of Troyius to end the ongoing conflict. The U.S.S. Enterprise was assigned to ferry her to Troyius, as well as provide her time to learn the customs of her new world.

A petulant individual unaccustomed to respecting others, she critically wounded her tutor with a dagger. Enterprise Captain James T. Kirk was then forced to assume the role of her tutor. Unaware of Elasian physiology, Kirk allowed her tears to touch his skin. The tears of Elasian women are a powerful biochemical aphrodisiac, rendering the "target" helplessly in love with the source of the tears. After a Klingon attempt to destroy the Enterprise, Elaan recognized her duty and was ultimately delivered to Troyius to fulfill her obligation. Kirk ultimately overcame the effects of her tears.