There is one authentic fulfilled Priesthood. The Priesthood of Jesus Christ.
There are different “shares” into or “participations” of or “koinonia” of that ONE Priesthood of Jesus’.
- The priesthood of all believers (that’d be Baptized people like you and I).
- The ministerial priesthood. That is like your Priest at the Parish.
- The Episcopacy. The Bishop’s office. An example of that is your diocesan Bishop.
In fulfillment of Exodus 19 (as David already appropriately pointed out), we see St. Peter teach us . . . .
1st PETER 2:7-9 7 To you therefore who believe, he is precious, but for those who do not believe, “The very stone which the builders rejected has become the head of the corner,” 8 and “A stone that will make men stumble, a rock that will make them fall”; for they stumble because they disobey the word, as they were destined to do. 9 But you are a chosen race,
a royal priesthood, a holy nation, God’s own people, that you may declare the wonderful deeds of him who called you out of darkness into his marvelous light.
CCC 1141 The celebrating assembly is the community of the baptized who, "by regeneration and the anointing of the Holy Spirit, are consecrated to be a spiritual house and a holy priesthood, that through all the works of Christian men they may offer spiritual sacrifices."9 This “
common priesthood” is that of Christ the sole priest, in which all his members participate:10
Mother Church earnestly desires that all the faithful should be led to that full, conscious, and active participation in liturgical celebrations which is demanded by the very nature of the liturgy, and to which the Christian people, “a chosen race, a royal priesthood, a holy nation, a redeemed people,” have a right and an obligation by reason of their Baptism.11
Bold Scripture & CCC above mine
I hope this helps.
God bless.
Cathoholic