Are there other levels of authority that I’m not aware of and are holy orders are required for these positions within the Church?
It depends what you’re asking about. For instance, religious orders may have abbots, abbesses, superiors general, and so on. These are all positions of authority within the order, and while I don’t think holy orders are generally a requisite, there may be individual orders where it is needed. “Monsignor” is an honorific title given by the Holy See – I think it’s only given to priests, but it’s not really a “level of authority,” so I’m not sure if it falls within the ambit of your question.
Certain bishops are, by custom or special concession, called “primates,” “patriarchs,” and “metropolitans.” A
primate is typically the bishop of the oldest diocese in a country.
Patriarchs are either the top bishops of certain Eastern Catholic churches, or in the Roman church they are the bishops of the sees of Venice, Lisbon, Jerusalem, and the East Indies, which have the title of patriarchate by ancient custom. A
metropolitan is the head of an ecclesiastical province (a group of neighboring dioceses); he is the archbishop of the province’s archdiocese, and the other dioceses are called
suffragans. For instance, Archbishop Timothy Dolan of New York is the metropolitan of a province which includes the dioceses of Brooklyn, Buffalo, Albany, and other places in the state of New York. The metropolitan has extremely limited authority over his suffragan dioceses, mostly applicable when the position of bishop of one of the suffragan dioceses is vacant.
And certain regions are not yet part of any diocese – for instance, mission territories and frontier lands – and they come under the jurisdiction of a Vicar Apostolic or Prefect Apostolic who is appointed by the Holy See similar to how a diocesan bishop is. He would always be a priest, if not in fact a bishop.
Other than that, I can’t really think of anything of significance that would suit your question.
