As you come to him, a living stone rejected by men but in the sight of God chosen and precious, you yourselves like living stones are being built up as a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ… But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light. Once you were not a people, but now you are God’s people; once you had not received mercy, but now you have received mercy. 1 Peter 2:4-5,9-10 (ESV)
Grace to you and peace from him who is and who was and who is to come, and from the seven spirits who are before his throne, and from Jesus Christ the faithful witness, the firstborn of the dead, and the ruler of kings on earth. To him who loves us and has freed us from our sins by his blood and made us a kingdom, priests to his God and Father, to him be glory and dominion forever and ever. Amen. Rev 1:4-6 (ESV)
Worthy are you to take the scroll and to open its seals, for you were slain, and by your blood you ransomed people for God from every tribe and language and people and nation, and you have made them a kingdom and priests to our God, and they shall reign on the earth. Rev 5:9-10 (ESV)
We, the body of Jesus, are the replacement of the Levitical priesthood. No longer do we need someone to be the human intermediary between us and God, we have Jesus. No longer do people need a priest to talk to God, they have you or can go to Him directly. And people should be able to see God through us, His priesthood.