What does it mean for Jesus to be our priest?

Jesus, the Christ, is regarded as our “Saviour” and so he is. The Bible, however, tells us that Jesus performed a number of roles that were and are essential to his role as Messiah. One of those roles is High Priest. This role is one that is clearly described in the Old Testament of the Bible, but applied to Jesus after his resurrection from the dead.
A priest is one who is appointed to minister and intercede to God on behalf of the people. In the early chapters of the Bible and before the Law of Moses was established, individuals performed the role of priest, such as Abel (Genesis 4), and Abraham (Genesis 12-13). When the children of Israel left Egypt and came to Mount Sinai, the LORD God gave them a Law through Moses and declared the descendants of Aaron, Moses’ brother, to be the line of the High Priests (Exodus 28). The Priests had to meet very rigid standards, wear special garments, adhere to special ritual observances and offer specific sacrifices (Exodus 28-29; Leviticus 1-8; 21).
In the New Testament, it is through the sacrificial death of Jesus that he has become the High Priest and mediator between God and humanity. He is the High Priest of our confessions and has been appointed by God.
“Since then we have a great high priest who has passed through the heavens, Jesus, the Son of God, let us hold fast our confession. For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin.”
Hebrews 4:14-15 ESV
Since Jesus offered himself as a sacrifice and he now lives forever, he does not need to offer continual sacrifices. Because he had a nature like ours (human nature) he is able to sympathize and relate to us, making him the perfect High Priest.
For every high priest chosen from among men is appointed to act on behalf of men in relation to God, to offer gifts and sacrifices for sins. He can deal gently with the ignorant and wayward, since he himself is beset with weakness. Because of this he is obligated to offer sacrifice for his own sins just as he does for those of the people. And no one takes this honor for himself, but only when called by God, just as Aaron was. So also Christ did not exalt himself to be made a high priest, but was appointed by him who said to him, “You are my Son, today I have begotten you”; as he says also in another place, “You are a priest forever, after the order of Melchizedek.”
Hebrews 5:1-6 ESV
And every priest stands daily at his service, offering repeatedly the same sacrifices, which can never take away sins. But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God, waiting from that time until his enemies should be made a footstool for his feet. For by a single offering he has perfected for all time those who are being sanctified.
Hebrews 10:11-14 ESV
The Old Testament, and particularly the Law of Moses established the role of High Priest, but with limitations because of human weakness of the Priests themselves. Jesus took on the role of High Priest for all people that would come to him. Although his nature was human, Jesus was sinless. As a sinless sacrifice and by willingly going to the cross for the sins of the people, Jesus rose to eternal life. He now makes intercession for the believers to God, the Father. Because he offered himself once for all time, those who come to him and make confession are forgiven their sins by one, single sacrifice.
Jesus is indeed our High Priest and mediator, but in order to benefit from his sacrifice, one must come into covenant relationship with him in order to be their High Priest.
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