I wouldn't envision anything that is different from the process currently followed for appointments to the Supreme Court. Correct me if I'm mistaken about the process, but as I understand it, that appointment rests with the Prime Minister throughout.
I am not entirely sure what the status is of a hearing before Parliament, but there is even greater value with the appointment of the Governor General than there is in following that process for a Supreme Court nominee, because it's much more relevant for the function of the Governor General to hear from parliamentarians as to what they expect from a Governor General. This is an opportunity for a face-to-face interaction directly with members of Parliament that would not occur subsequently in the tenure of the Governor General.
I'm not proposing any sort of hearing where anyone has any veto over the proposal or anything like that. I'm just suggesting that there is some value in a face-to-face meeting in the House prior to taking office.