Hebrews 8:4

Now if he were on earth, he would not be a priest at all, seeing there are those who offer gifts according to the law.

Jesus could not have been a priest on earth because he did not belong to the priestly family, nor even to the tribe from which that family descended. Christ's priesthood was of a different order altogether, being after the order of Melchizedek. The importance of this is in the bearing it has on the purpose for which the Son of God came into the world. It had absolutely nothing to do with being a priestly Messiah on earth, as some supposed; nor was it to reign upon the earth as a secular monarch. Dr. James D. Bales noted that "Christ could not possibly have been crowned king on earth during his personal ministry, since the law could not have been taken away prior to his death (Colossians 2:14; Ephesians 2:13-16)."[6] Bales indicated the true reason why Jesus came, not to be priest, not to reign as a literal king on a throne on earth, "but to put away sin by the sacrifice of himself" (Hebrews 9:26,27).