John wrote about Christ:

Rev 1:6
And hath made us KINGS and PRIESTS unto God and his Father; to him be glory and dominion for ever and ever. Amen.

The 4 living Creatures and the 24 Elders proclaimed:

Rev 5:10
And hast made us unto our God KINGS and PRIESTS: and we shall reign on the earth.

(Think of Melchi-Zedek: King of Righteousness. King of Salem and Priest of the Most High God)

Apostle Peter wrote:

1 Peter 2:9
But ye are a chosen generation, a ROYAL PRIESTHOOD, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light;

1 Peter 2:5
Ye also, as lively stones, are built up a SPIRITUAL HOUSE, an HOLY PRIESTHOOD, to offer up SPIRITUAL SACRIFICES, acceptable to God by Jesus Christ.

Paul wrote about these Royal Priests, they are the Congregation of the First Born of the Dead, the Assembly of the Spirits of the "RIGHTEOUS" Men made perfect, dwelling in Heavenly Jerusalem. (The Greek Word dikaios in Hebrew 12:23 below means "Righteous")

Hebrews 12
22 But ye are come unto mount Sion, and unto the city of the living God, the HEAVENLY JERUSALEM, and to an innumerable company of angels,
23 To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just (DIKAIOS) men made perfect

Jeremiah about Christ and New Jerusalem:

Jer 23
5 ... I will raise unto David a RIGHTEOUS Branch, and a King shall reign and prosper, and shall execute judgment and justice in the earth.
6 In his days Judah shall be saved, and Israel shall dwell safely: and this is HIS NAME whereby he shall be called, The Lord OUR RIGHTEOUSNESS.

Jer 33:
15 ... will I cause the Branch of RIGHTEOUSNESS to grow up unto David; and he shall execute judgment and RIGHTEOUSNESS in the land.
16 In those days shall Judah be saved, and Jerusalem shall dwell safely: and this is THE NAME wherewith she shall be called, The Lord OUR RIGHTEOUSNESS.
17 For thus saith the Lord; David shall never want a man to sit upon the throne of the house of Israel;
18 Neither shall THE PRIESTS THE LEVITES want a man before me to offer burnt offerings, and to kindle meat offerings, and to do sacrifice continually.

Christ said about the Royal Priests:

Revelation 3:12
Him that overcometh will I make a pillar in the temple of my God, and he shall go no more out: and I will write upon him the name of my God, and the name of the city of my God, which is NEW JERUSALEM, which cometh down out of heaven from my God: and I will write upon him MY NEW NAME.

Christ is called Faithful and True, does the same passage imply that he is also called Righteous (the Hebrew name Zadok)?

Revelation 19:
11 And I saw heaven opened, and behold a white horse; and he that sat upon him was called Faithful and True, and in RIGHTEOUSNESS he doth judge and make war.

1 John 2:1
... And if any man sin, we have an advocate with the Father, Jesus Christ THE RIGHTEOUS:

Psalm 34:
19 Many are the afflictions of THE RIGHTEOUS: but the Lord delivereth him out of them all.
20 He keepeth all his bones: not one of them is broken.

Psalm 118:
15 The voice of rejoicing and salvation is in the tabernacles of THE RIGHTEOUS: the right hand of the Lord doeth valiantly.
16 The right hand of the Lord is exalted: the right hand of the Lord doeth valiantly.
17 I shall not die, but live, and declare the works of the Lord.
18 The Lord hath chastened me sore: but he hath not given me over unto death.
19 Open to me the gates of RIGHTEOUSNESS: I will go into them, and I will praise the Lord:
20 This gate of the Lord, into which THE RIGHTEOUS shall enter.
21 I will praise thee: for thou hast heard me, and art become my salvation.
22 The stone which the builders refused is become the head stone of the corner.
23 This is the Lord's doing; it is marvellous in our eyes.
24 This is the day which the Lord hath made; we will rejoice and be glad in it.
25 Save now, I beseech thee, O Lord: O Lord, I beseech thee, send now prosperity.
26 Blessed be he that cometh in the name of the Lord: we have blessed you out of the house of the Lord.
27 God is the Lord, which hath shewed us light: bind the sacrifice with cords, even unto the horns of the altar.

In Ezekiel's Temple, only the Levites who are of the Seed of Zadok can come near the Lord to minister on His Altar:

Ezek 48:11
It shall be for the priests that are sanctified of the sons of Zadok; which have kept my charge, which went not astray when the children of Israel went astray, as the Levites went astray.

Christ stated that the Martyrs shall be his Sons:

Revelation 21
7 He that overcometh shall inherit all things; and I will be his God, and he shall be my son.

ISAIAH 66
5 ... Your brethren that hated you, that cast you out for my name's sake, said, Let the Lord be glorified: but he shall appear to your joy, and they shall be ashamed.

ISAIAH 66
21 And I will also take of them for priests and for Levites, saith the Lord.