“But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises.”
King James Version (KJV)
8:6 And now he hath obtained a more excellent ministry - His priesthood as much excels theirs, as the promises of the gospel (whereof he is a surety) excels those of the law. These better promises are specified, #Heb 8:10|,11: those in the law were mostly temporal promises.
Heb 8:6 Now hath he obtained a more excellent ministry. More excellent than that of the Levitical priesthood. He serves in the heavenly sanctuary. He is the meditator. The high priest was a mediator, interceding with God for the people. Christ is the mediator of a better covenant with its more glorious promises; viz., the Gospel.