Was Melchizedek a priest under the law or from the tribe of Levi?
Melchizedek was not a priest under the law, nor was he of the tribe of Levi. He was a high priest forever and a priest of all, covering the whole human race. Christ is a high priest after the order of Melchizedek, not Aaron.
Les explains that Melchizedek was not a priest under the law and was not from the tribe of Levi. He came from Salem, or Shalom, the city of peace, which is Jerusalem, and he was a high priest forever. His priesthood was not limited to Israel but covered the whole spectrum of the human race. Therefore Christ is not a high priest after the order of Aaron, but after the order of Melchizedek. That means Christ is not merely the high priest of the Jew, but the high priest of whomever we might be. Les also connects this to Hebrews 9, where Christ became a high priest of good things to come by a greater and more perfect tabernacle, contrasting the earthly pattern shown to Moses with the heavenly reality.