But this man - Greek "But he" - referring to Christ.
Because he continueth ever - Greek "Because he remains forever." The idea is because he does not die, but ever lives, he has an unchanging priesthood. There is no necessity that he should yield it to others, as was the case with the Jewish priests because they were mortal. The reason in their case, why it passed to others, was not that they did not perform the office well, but that they were mortal, and could not continue to hold it. But this reason could not operate in the case of the Lord Jesus, and therefore his priesthood would be permanent.
Hath an unchangeable priesthood - Margin, "or, "which passeth not from one to another." The margin expresses the sense of the passage. The idea is not strictly that it was "unchangable," but that "it did not pass over into other hands." The Levitical priesthood passed from one to another as successive generations came on the stage of action. This reasoning is not designed to prove that the priesthood of Christ will be literally "eternal" - for its necessity may cease when all the redeemed are in heaven - but that it is permanent, and does not pass from hand to hand,

But this - Ὁ δε, But he, that is, Christ, because he continueth ever - is eternal, hath an unchangeable priesthood, απαραβατον ἱερωσυνην, a priesthood that passeth not away from him; he lives for ever, and he lives a priest for ever.

But this [man], because he continueth ever, hath an (i) unchangeable priesthood.
(i) Which cannot pass away.

But this man, because he continueth ever,.... Though he died, death did not forbid him to continue, as it does other men; he was not forced to die, he died voluntarily; and he continued but for a small time under the power of death; besides, his death was a branch of his priestly office: so that he not only continued in his divine nature, which still had the human nature in union with it, but he continued in his office as a priest, and quickly rose from the dead; and the virtue of his sacrifice always remains, and he himself ever lives as an intercessor: wherefore he
hath an unchangeable priesthood; which will never be antiquated, and give place to another; nor does it, or ever will it pass from him to another, for it is needless, seeing he lives, and no other is sufficient for it; and it would be injustice to pass it to another; the glory of it is due to him; and this is matter of comfort to the saints, that he sits a priest upon his throne, and that his priesthood always continues.

he--emphatic; Greek, "Himself." So in Psalm 110:4, "THOU art a priest"; singular, not priests, "many."
continueth--Greek, simple verb, not the compound as in Hebrews 7:23. "Remaineth," namely, in life.
unchangeable--Greek, "hath His priesthood unchangeable"; not passing from one to another, intransmissible. Therefore no earthly so-called apostolic succession of priests are His vicegerents. The Jewish priests had successors in office, because "they could not continue by reason of death." But this Man, because He liveth ever, hath no successor in office, not even Peter (1-Peter 5:1).

He continueth for ever - In life and in his priesthood. That passeth not away - To any successor.