...a minister of Christ Jesus to the Gentiles in the priestly service of the gospel of God...
Romans 15:16 ESV

There are at least 4 orders of priesthood described in the Bible.

1. Before Sinai, each family had its own priest for the family’s altar and religious life. God recognized that priesthood as valid when he gave instructions for them in Exo 19:22 before Levi had been set apart.
2. All Israel was commissioned by God at Sinai to be a nation of priests, and all true disciples of Yeshua are ordained into this priesthood when they repent of sin and submit to him. See Exo 19:6 and Rev 1:6.
3. God set apart the tribe of Levi to serve a priestly function for the whole nation of Israel, and the sons of Aaron to be full priests in service at his altar. See Lev 8-9 and Num 18.
4. There is a type of priest-king, of which Melchizedek is the exemplar in Genesis 14, and of which Yeshua is the highest example.