If Elsa is re-apped without her memories, the slate will be wiped clean. She will not regain her mountain god runes.

If Elsa is re-apped with memories, she may either retain her runes or regain them once she begins re-transforming.

Either way, if you were not in-game when we offered monster rerolls, you may also opt to reroll Elsa's monster type if you so wish! (Or you can keep the old one.)