The Mediator of a Better Covenant
The writer of Hebrews draws a sharp contrast between the Levitical priesthood and the ministry of Jesus. We see this explicitly in Hebrews 8:6, where the superiority of Christ's work is defined by the quality of the covenant He mediates.
Hebrews 8:6 (MOUNCE Interlinear)
"Now at present, he [Christ] has obtained a superior [diaphorōteras] ministry [leitourgias] the covenant [diathēkēs] he mediates [mesitēs] is better [kreittonos], since it is enacted [nenomothetētai] on better promises [epangeliais]."
The word diaphorōteras (more excellent) implies a difference not just in degree, but in kind. "For if that former, first in time, existed blameless, no occasion would be sought for a second" (Hebrews 7:). The new superior ministry is distinct and surpassing, "In speaking of a new [covenant] the first is made old. Now that made old also to be ready to disappear" (Hebrews 8:13).
The old has been made old, Christianity has make that distinction in the arrangement of the books in the Bible, Old Testament and New Testament for this reason. We look at the old in light of the new, in Jesus who exists Light and Life, the reality of the shadow and exists the mediator of a superior ministry.
"they [priests] serve in a shadowy model of the heavenly just as Moses warned about, to erect the tabernacle "for he said 'see that you do all according to the pattern shown on the mountain'" (Hebrews 8:5)
The Old testament was a shadow of that to come. To go back to the old, and to live to its written code is to sever from Christ and fall from grace (Galatians 5:4). This is not just in regards to justification, but also elemental principles, dietary laws, sabbaths days, festivals... things destined to perish (Colossians 2:16). See, From Shadow to Substance: The Peril of Returning to the Old Covenant.
The Old Covenant was a contract based on "if you do, then I will bless." It as Paul said it has a curse, break one break it all. It depended on human performance, which ultimately failed because of the carnal nature of mankind. The New Covenant is "better" because it depends on the performance of the Mediator, Jesus, who cannot fail.
From External Code to Internal Reality
The failure of the Old Covenant was not a flaw in God's Law, but in the people's inability to keep it. As noted in articles from Love Fulfilled Ministry, "In the new covenant, God does what the Law could not: He writes His laws on hearts and minds." This aligns perfectly with the prophecy of Jeremiah quoted in Hebrews 8.
Hebrews 8:10 (ESV Interlinear)
"For this is the covenant [diathēkēs] that I will make with the house of Israel after those days, declares the Lord: I will put my laws into their minds [dianoian], and write [epigrapsō] them on their hearts [kardias], and I will be their God, and they shall be my people."
Under the old system, the law was written on stone tablets—external and cold. It demanded righteousness but gave no power to achieve it. In the New Covenant, the Spirit of God moves the location of the law from stone tablets to the human heart. This is the "superior ministry": it changes the nature of the worshiper rather than just their behavior. God puts his Spirit within, this new living way walks in line with God's Spirit fulfilling his righteous requirements.
Application
The implication of this truth is profound for us today. Many believers still struggle as if they are under the Old Covenant, trying to earn God's favor through external discipline alone. However, the superior ministry of Christ invites us to rest in His work.
Because Jesus is the mesitēs (mediator) who stands between us and the Father, our standing is secure. We do not obey to get saved; we obey because we are changed. The desire to please God is now an internal instinct, written on our hearts, rather than an external pressure. When we fail, we do not look to a system of animal sacrifices, but to the "better promises" of a mediator who can cleanse us from all unrighteousness.
Hebrews 8:12 (ESV Interlinear)
"For I will be merciful [hileōs] toward their iniquities, and I will remember [mnēsthō] their sins no more."
Conclusion
The ministry of the New Covenant is superior because it accomplishes what religion never could: actual intimacy with God and maturity in Christ. By replacing the shadow with the substance of Christ, God has enacted a system based on grace, guaranteed by a perfect Mediator, and authenticated by the internal transformation, through Spirit and Word, of His people.
We are no longer servants looking at the law from the outside, but children with the nature of the Father written on the inside. Our hearts exist epistles themselves, as Paul writes, God is writing on them, not in ink, nor on hearts of stone (not the letter or written code of commands on stone or parchment or paper) but on a heart of flesh, the Spirit of the living God writes his laws on tablets of human hearts (2 Corinthians 3:2-3).