The writer of Hebrews is building one of his arguments that we are no longer under the Old Law. The Jews saw Psalms 110 as being Messanic and it states in verse 4 that the Messiah will be a high priest after the order of Melchizedek. The Writer of Hebrews argues that if we are still under the Law that would not be possible because the high priest came from the tribe of Levi and the Messiah was to be from the tribe of Judah, in the line of David. So, for the Messiah to be both king and high priest we have to be under a new covenant! The phrase ‘without beginning of days or end of life’ simply relates to the fact that there is no biblical history for the beginning or the end of Melchizedek’s priesthood as there was for other priests in the Old Testament history. God developed the unique personality of Melchizedek and had him encounter Abraham to build a blueprint of Christ and His priesthood. Jesus is a kingly, righteous, peaceful priest who is unique in that His priesthood was original. He will forever be a priest of God Most High! Just the very High Priest we need to intercede for for you and me.