8:7 For if that first covenant had been faultless, no one would have looked for a second one. 8:8 But showing its fault, God says to them,
“Look, the days are coming, says the Lord, when I will complete a new covenant with the house of Israel and with the house of Judah.
8:9 “It will not be like the covenant that I made with their fathers, on the day when I took them by the hand to lead them out of Egypt, because they did not continue in my covenant and I had no regard for them, says the Lord.
8:10 “For this is the covenant that I will establish with the house of Israel after those days, says the Lord. I will put my laws in their minds and I will inscribe them on their hearts. And I will be their God and they will be my people.
8:11 “And there will be no need at all for each one to teach his countryman or each one to teach his brother saying, ‘Know the Lord,’ since they will all know me, from the least to the greatest.
8:12 “For I will be merciful toward their evil deeds, and their sins I will remember no longer.”
8:13 When he speaks of a new covenant, he makes the first obsolete. Now what is growing obsolete and aging is about to disappear.

According to Jesper Svartvik:

‘These words in Hebrews are a cornerstone of Christian supersessionist theology: the people of Israel no longer find favor with the God of Israel because God has made a new declaration of love to the Christian church.’ (Emphasis added)

Allen (NAC, Introduction) comments:

‘There is no anti-Judaic polemic in the epistle. Hebrews does not address the issue of Jew/Gentile relationships…With respect to replacement theology or supersessionism, one will not find in Hebrews any notion that the Jewish people have been replaced by any other group, including the church. However, and this is crucial, it is clear there is a form of supersessionism in Hebrews. It is vital that this notion be defined properly. In Heb 8:13 the old covenant is superseded by the new. But this point is made by the author in his appeal to the Old Testament Scriptures themselves, namely Jer 31:31–33, which predicts this very thing. The author of Hebrews is arguing that Jesus has inaugurated the new covenant in fulfillment of Jeremiah’s prophecy.’ (Emphasis added)

Phillip Long insists that the author of Hebrews:

‘does not argue Israel has been replaced and all, but that the promises made to Israel, including the New Covenant, have their fulfillment in Jesus the Messiah.’

Gavin Ortlund points out that the apparent supersessionism of this passage should be read in the light of what comes later in the epistle:

‘Markus Bockmuehl helpfully points out that the alleged supersessionism of the early and middle chapters of Hebrews is seriously tempered by the later chapters, and particularly chapter 11, with its appeal to old covenant believers as the “great cloud of witnesses” who exemplify faith in God to the new covenant community.

‘“The undoubtedly supersessionist flavour of Heb. 8 and 9 is seriously misread of one takes it as the author’s general theological principle for the heritage of Israel and of the Old Testament. As the context of those chapters makes clear, the claim of obsolescence is in fact highly specific in its application, and concerns primarily the Old Covenant’s cultic apparatus of atonement…. The superiority of the New Covenant introduces not a new people of God so much as a newly energized worship of God – constituted around the definitive and permanently efficacious sacrifice. It is that difference in which the discontinuity of the covenants subsists, not in the identity of the people of God or even in their faith.”’