akagami no shirayukihime
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A 2006-present shoujo manga written by Akizuki Sorata, published by Hakusensha. An anime was green-lit to air for the summer 2015 season.
Wikipedia Summary
Shirayuki is a normal citizen of the kingdom of Tanbarun with one unique feature: her red hair. When the prince of Tanbarun orders her to become his concubine because of this, she cuts her hair and escapes to the neighboring kingdom of Clarines. On her way there, she meets and befriends Prince Zen and his two aides. When Zen is poisoned by an apple meant for her, Shirayuki successfully obtains the antidote and decides to accompany the trio to Clarines. Shortly thereafter, Shirayuki passes an exam for a position to train in the palace as a pharmacist. The story follows Shirayuki and her friends as she finds her place in Clarines and carries out her duties as a court pharmacist.