When she joins the Seven Mothers, she will do so initially as a Lay Member. The temple will work to guide her towards an understanding of the Seven Mothers and the Red Moon. They will help her see what runes are in line with particular aspects of the Seven Mothers and which deviate. Ultimately, when the temple priestesses determine that she is ready, she will be initiated, freeing herself from an old rune and adopting the new one (so will still have 3).
The Moon rune has the benefit of being both an elemental rune and a form or power rune (i.e. Balance). An Earth/Dark or even Fire/Light rune might easily shift to a Moon rune. The shifting Water rune could align to the cycles of the Moon. Someone strong in the Air rune would have to recognize that the uncontrolled, violent ways of Storm are harmful and wishes to control those urges. Just as the Moon ascended into the Middle Air and contests that realm, the initiate strong in the Air rune, could overcome that to become stable and balanced — however, I suspect the trials and tests of such a person would be much more difficult, probably along the pathways of Danfive Xaron. The Moon rune could also replace a power rune, so instead of having a Death rune, the person has come to accept the balance of Life and Death.
.
