It won’t wait until the nomination, it will be June 7 when Donald Trump passes 1237 delegates.
Priebus has already stated he won’t be returning next year as head of the RNC. But I expect him to step down shortly after June 7 because he has allowed Romney to call the shots in using Cruz to stop Trump.
He might if Cruz is the nominee. If Trump is the nominee, I expect Priebus will stay on until after the election to make sure Trump doesn't install his own people at the RNC.