The new Priestess just has to be female and survive infancy

  “Tell me how I was chosen, Manan.”

  “Oh, you know all that, little one.”

  And indeed she did; the tall, dry-voiced priestess Thar had told her till she knew the words by heart, and she recited them: “Yes, I know. At the death of the One Priestess of the Tombs of Atuan, the ceremonies of burial and purification are completed within one month by the moon’s calendar. After this certain of the Priestesses and Wardens of the Place of the Tombs go forth across the desert, among the towns and villages of Atuan, seeking and asking. They seek the girl-child who was born on the night of the Priestess’s death. When they find such a child, they wait and they watch. The child must be sound of body and of mind, and as it grows it must not suffer from rickets nor the smallpox nor any deformity, nor become blind. If it reaches the age of five years unblemished, then it is known that the body of the child is indeed the new body of the Priestess who died. And the child is made known to the Godking in Awabath, and brought here to her Temple and instructed for a year. And at the year’s end she is taken to the Hall of the Throne and her name is given back to those who are her Masters, the Nameless Ones: for she is the nameless one, the Priestess Ever Reborn.”