the function of any priest: to offer sacrifice!
public worship requires a priest offering sacrifice at an altar!
Sacrificing what, exactly? The OT priestly sacrifices were for sin, but that has been done away with:
Heb 10:11 And every priest stands daily at his service, offering repeatedly the same sacrifices, which can never take away sins.
Heb 10:12 But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God,
Heb 10:13 waiting from that time until his enemies should be made a footstool for his feet.
Heb 10:14 For by a single offering he has perfected for all time those who are being sanctified.
Heb 10:15 And the Holy Spirit also bears witness to us; for after saying,
Heb 10:16 “This is the covenant that I will make with them after those days, declares the Lord: I will put my laws on their hearts, and write them on their minds,”
Heb 10:17 then he adds, “I will remember their sins and their lawless deeds no more.”
Heb 10:18 Where there is forgiveness of these, there is no longer any offering for sin. (ESV)
As for the sacrifices of believers in general, the royal priesthood:
Rom 12:1 I appeal to you therefore, brothers, by the mercies of God, to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship. (ESV)
Eph 5:2 And walk in love, as Christ loved us and gave himself up for us, a fragrant offering and sacrifice to God. (ESV)
Php 4:18 I have received full payment, and more. I am well supplied, having received from Epaphroditus the gifts you sent, a fragrant offering, a sacrifice acceptable and pleasing to God. (ESV)
Heb 13:15 Through him then let us continually offer up a sacrifice of praise to God, that is, the fruit of lips that acknowledge his name.
Heb 13:16 Do not neglect to do good and to share what you have, for such sacrifices are pleasing to God. (ESV)