The 6 and 7th ch of Hebrews makes reference to the priestly office of Christ; that He was a "Priest forever' according to the office of Melchizedek. In ch 7 we can see:
22 By so much was Jesus made a surety of a better testament (or covenant). 23 And they truly were many priests, because they were not suffered to continue by reason of death: 24 But this
man, because he continueth ever, hath an unchangeable priesthood. 25 Wherefore he is able also to save them gto the uttermost hthat come unto God by him, seeing he ever liveth to make intercession for them.
The Holy Bible: King James Version, Electronic Edition of the 1900 Authorized Version. (Bellingham, WA: Logos Research Systems, Inc., 2009), Heb 7:22–25.
It would seem odd if this passage were speaking of the NC and not the C of G in general.
Poole:
"22 By so much was Jesus made a surety of a better testament.
This brings in the consequent on ver. 20.
As much excellency as was in God’s oath constituting,
so much there must be in the office constituted. The Aaronical priesthood, by God’s constitution, was excellent; but Christ’s is much more so, being by God’s oath made personal and everlasting, relating to the best covenant;
so as the Hebrews had the greatest reason to renounce Aaron’s, and to cleave to Christ’s for salvation. He being God-man, is a Surety, one that bindeth himself for another, to see something paid or performed, to give security for another; and is proper to him as a Priest, Job 17:3; Psal. 119:122: Prov. 6:1. In the Mosaical economy the priests were typical sureties, or undertakers for the people; so Aaron, as a surety, was sent by Moses to stand between the living and the dead, when God was cutting off those sinners, Numb. 16:46, 48. The Spirit interprets this
Surety to be a
Mediator, chap. 8:6, which is the general comprehensive name of all his offices: as he gives all from God to us in and
by his promises, he is
the Testator fulfilling them, chap. 9:15, 16; as he gives satisfaction to God for us, and returns our duty performed with the incense of his merits, he is our
Surety; which merit of his
resulted from his perfect obedience to the whole law and will of God, and from
the full satisfaction he made to God by his death for our sins, Rom. 5:19; 2 Cor. 5:21; Gal. 3:13.
A better testament; the gospel covenant, described chap. 8:10–12, and
referreth to what the Lord foretold of it, Jer. 31:33, 34, which is better than the Mosaical for perspicuity, freeness, fulness, spirituality, and the Spirit promised in it
for its ratification by the death of Christ, and its perpetuity: see chap. 8:8, 9, 11.
Matthew Poole,
Annotations upon the Holy Bible, vol. 3 (New York: Robert Carter and Brothers, 1853), 840.
The gospel economy dates back to gen 3; the death of Christ was the consummating moment and 'ratification'.
11 But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building; 12 Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption
for us. 13 For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh: 14 How much more shall the blood of Christ, who
through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
The Holy Bible: King James Version, Electronic Edition of the 1900 Authorized Version. (Bellingham, WA: Logos Research Systems, Inc., 2009), Heb 9:11–14.