The removal of priesthood authority in the messianic age is expressly denied in scripture on the basis of divine covenant - not just God’s covenant with men, but the covenant of the Father and the Son. This is a covenant between two divine parties, neither of whom can violate or alter any term of that covenant. The text that proves this is the entire argument of Jeremiah 33, which begins with a prophecy of the messiah coming, restoring the Kingdom so that the “voice of the bride and the voice of the bridegroom” (33:11) return to the land. (cf. John 3:29.) Then the messiah takes up his kingship and becomes inheritor of the Davidic covenant, which contains these terms:
For thus saith the LORD; David shall never want a man to sit upon the throne of the house of Israel; Neither shall the priests the Levites want a man before me to offer burnt offerings, and to kindle meat offerings, and to do sacrifice continually. And the word of the LORD came unto Jeremiah, saying, Thus saith the LORD; If ye can break my covenant of the day, and my covenant of the night, and that there should not be day and night in their season; Then may also my covenant be broken with David my servant, that he should not have a son to reign upon his throne; and with the Levites the priests, my ministers. As the host of heaven cannot be numbered, neither the sand of the sea measured: so will I multiply the seed of David my servant, and the Levites that minister unto me. (Jer 33:17-22)
I can’t imagine how much more clearly the point could be made. Here was have a text that is about the Messianic kingdom, which interprets the Messiah’s rule of Israel. It verifies the continuance of the priesthood as a fulfillment of the Levitical covenant, a term of the covenant with David, and ensures both claim on the basis of the creation covenant. Three of the five covenants God makes in the Old Testament are invoked here, so that God basically invests his entire credibility as a covenant-maker on the perpetuity of the priesthood in Zion, effective upon the coming of the messiah. Moreover, there can be no contingency to the fulfillment of these promises, since they are made with Christ, who cannot violate the terms of the covenant and forfeit these promises. It would require a break in the relationship of the Father and Son - a dissolution of the godhead - to remove the priesthood from the earth.
The real question is for you: Why do you assume that continual scriptural revelation is necessary for the Church? Can you find that taught in scripture? Is not your source for this assumption the fact that Mormonism claims that there must always be scriptural revelation? If so, then you have not posed a real problem for us, since the dilemma only arises from presupposing a Mormon understanding of revelation. It is a sufficient answer merely to note that we do not grant the assumption that makes this question a problem.
That is a sufficient answer, but not the only answer, nor even the best. Rather, there is warrant from Scripture itself so show that the presence of continual scriptural revelation is not intrinsic to the operations of divine authority. For instance, we have no reason to believe that there was any Scripture in the time of the patriarchs or before them. There were divine covenants and valid priestly offerings, but no special texts. (Of course, Mormonism claims Abraham wrote scripture, but again, you would have to appeal to your own principles, assuming Mormonism from the outset in order to make that argument.) Moreover, even on Mormon assumptions, we know that there was a Levitical priesthood operating in Israel during the so-called intertestamental period. This is clear from the fact that Zacharias not only serves in the Temple but gets a revelation there in Luke 1.
Moreover, the New Testament teaches that “The law and the prophets were until John: since that time the kingdom of God is preached.” (Luke 16:16) This passage poses a problem for anyone who thinks that the same rules that make scriptural revelation normative in the Church would be the same in the new covenant as in the old. According to Catholicism, the reason there does not need to be new Scripture is that the definitive revelation of God is not a text but the person of Christ himself. The Incarnation as such contains all the truth that God has for man. This is not to say that it exhausts the truth and limits our potential knowledge, but the exact opposite: it points out that an infinite content has already been communicated by God. That is why the author of Hebrews writes, “God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets, Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds.” Clearly a change in the mode of divine speech is indicated here, and no theology about the nature of revelation can afford to overlook it. Yet your assumptions demand that we overlook it, for you are claiming a kind of eternal necessity for new scripture that does not fit with the Biblical teaching.
This does not mean God is silent, since he certainly speaks through the Church in the person of Christ, or that he is powerless, since he could hypothetically inspire more text. It does mean we have no right to assume that he must do so, as your question implies. The real issue about the canon, after all, has never been about whether God still speaks, but *how *he does so.