By what authority is one called a priest, in Christianity?

By what authority is one called a priest, in Christianity?

God calls a Godly man of a household...a priest

catholics have their rules of law.

not by the Bible which eliminated priesthood except for Jesus.
Jesus is the only Priest accepted by the Bible.
Hebrews.

By the authority which comes from the High Priest Christ Jesus entrusted to His Apostles and their successors (Bishops). So the authority is by Christ Jesus and His Church.

But even Catholics believe that all baptized Christians are part of the Priesthood.

To put it simply there is only one Priest Christ Jesus, the Bishops, Priests, and Deacons are His Ministers.

http://www.usccb.org/catechism/text/pt2sect2chpt3.shtml#art6

Every believer is a priest in Christianity although not in the order of Levi as were the Jewish priests under the law but in the order of Melchizedek.

You just touched upon a problem of some churches.

The Bible gives us Elders, and ministerial servants. Of course, these are defined with their Greek derivatives at times. Where they get the other titles from is at times a matter of organization, and at times a matter of apostasy.

Ministerial Servants;
12 KJV: Let the deacons be the husbands of one wife, ruling their children and their own houses well.
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12 Darby: Let the ministers be husbands of one wife, conducting their children and their own houses well:
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12 UMGreek: ?? SS's? AA?????? ??????, ??????????? ????? ?? ????? ????? ??? ???? ?????? ?????.

Elders:
17 KJV: Let the elders that rule well be counted worthy of double honour, especially they who labour in the word and doctrine.
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17 Darby: Let the elders who take the lead among the saints well be esteemed worthy of double honour, specially those labouring in word and teaching;
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17 UMGreek: ?? ????? ???????????? ??????????? ?? ?????????? ?????? ?????, ??????? ???? ??????????? ??? ????? ??? ???????????

A priest is one who makes sacrifices. The Jews had the Levites, the priestly tribe, who would make sacrifices upon the altar in the Temple in Jerusalem.

For Christianity, priests hold an "amanuensis" of the sacrifice of Jesus, although with his sacrifice, they no longer need to make them anymore. This is known as preserving the "sacerdotal" (sacrificial) order of the priests. This is the primary difference between a priest, and a pastor, or minister, who do not have this sacrificial connection.

There is more: At the Pentecost, the disciples there were filled with the Holy Spirit. They went out and "ordained" others to be priests, by laying on their hands, and transferring this gift of the Holy Spirit. They went on, and... all the way down to today. Priests (Roman Catholic, Anglican, some Lutherans, and others) preserve this "Apostolic Order" all they way back to the Pentecost.

So, priests are ordained, by a bishop, who was ordained by other bishops (3 or more), who lays his hands on the person, giving them the gift of the Holy Spirit.