Hebrews 8:4

For if he were on earth - As the Jewish temple was standing when this epistle was written, the whole temple service continued to be performed by the legal priests, descendants of Aaron, of the tribe of Levi; therefore if Christ had been then on earth, he could not have performed the office of a priest, being of the tribe of Judah, to which tribe the office of the priesthood did not appertain.

There are priests that offer gifts - This is an additional proof that this epistle was written before the destruction of Jerusalem. As the word θυσιαι, sacrifices, is not added here as it is in Hebrews 8:3, is it any evidence that bloody sacrifices had then ceased to be offered? Or, are both kinds included in the word δωρα, gifts? But is δωρον, a gift, ever used to express a bloody sacrifice? I believe the Septuagint never used it for זבח zebach, which signifies an animal offered to God in sacrifice.

For if he were on earth, he should not be a priest - He could not perform that office. The design of this is, to show a reason why he was removed to heaven. The reason was, that on earth there were those who were set apart to that office, and that he, not being of the same tribe with them, could not officiate as priest. There was an order of people here on earth consecrated already to that office, and hence, it was necessary that the Lord Jesus, in performing the functions of the office, should be removed to another sphere.

8:4 But if he were on earth - If his priesthood terminated here. He could not be a priest - At all, consistently with the Jewish institutions. There being other priests - To whom alone this office is allotted.