Adam Clarke on 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 Heb 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.