Christians: a chosen generation, a royal priesthood
But you are a chosen generation, a royal priesthood, a holy nation (2 Tim 1:9), His own special people, that you may proclaim the praises of Him who called you out of darkness into His marvelous light; who once were not a people but are now the people of God, who had not obtained mercy but now have obtained mercy. Beloved, I beg you as sojourners and pilgrims, abstain from fleshly lusts which war against the soul, having your conduct honorable among the Gentiles, that when they speak against you as evildoers, they may, by your good works which they observe, glorify God in the day of visitation.
All believers constitute a holy priesthood. Peter does not claim an exclusive priesthood vested in him, but his inspired testimony is that all members of the body of Christ, the living stones, are a priesthood. In the Old Testament the priesthood of Christ was foreshadowed in Aaron and the priesthood of believers by the sons of Aaron. No longer are needed sacrifices of animals, for He has brought the one sacrifice, by which he has made the new and living way by His blood into the Holiest, so that every believer can draw nigh with a true heart and full assurance of faith, with hearts sprinkled from an evil conscience and bodies washed with pure water (Hebrew 10:19-22). This completely disposes of the ritualistic priesthood, vested in "ordained" men, that system which has been and still is and always will be, the corruption of Christianity. It also answers the blasphemous mass, which is an act of idolatry.
The function of the holy priesthood of believers consists in bringing spiritual sacrifices acceptable to God by Jesus Christ. (Hebrews 13:15).
The royal priesthood of Christ, is the priesthood after the order of Melchisedec. He was the King-Priest who came to Abraham and made known God and His glory to Abraham. Thus in Christ we behold the glory of God and as identified with Christ, indwelt by Him, our royal priesthood is to make Him and His excellencies known among men. (See Hebrews 7)
In relation to Israel, we must not forget that there will be a future remnant of the nation, the nation which is now dispersed, which will become a holy nation, a royal priesthood in connection with the other nations
Arno Gaebelein's Annotated Bible