Hebrews 8-9 are theologically more controversial than the rest of Hebrews because it appears the writer of Hebrews says the Jewish people have been replaced by the Church. The New Covenant has replaced the Old just as Jesus’ sacrifice on the cross is superior to the old sacrifice in the Temple. As such, chapters 8 and 9 have been used to teach that the Jewish people are no longer God’s people and the church replaces them completely. This would therefore imply that any promises made to Israel in the Hebrew Bible are either cancelled or to be reinterpreted as applying to the Church.
The theological term for this is supersessionism, the view that church supersedes the Jews as the people of God. For some types of theology, the idea that the Jews were replaced by the Church is an assumption, the proof for which is found in Hebrews, especially chapters 8-9. This historic view argues the church is a new Israel and the promises of the Hebrew Bible are fulfilled in the church, often in a spiritual sense.
For example, Jeremiah 31 seems to indicate that at some point in the future, the city of Jerusalem would be rebuilt. Possibly this is fulfilled when some Jews return after the exile, but it may point to a future restoration of the Jews as well. But since this prediction is in the context of the New Covenant, older writers therefore re-interpreted spiritually.
The “wall great and high” is of no earthly material; the extension is not one of yards on miles, but of nations and ages; the consecration of the unclean places is but typical of the regenerative force of Christianity, which reclaims the moral wastes of the world, and purifies the carnal affections and sinful tendencies of human nature; and no material city could ever “stand for aye.” Only the kingdom and Church of Christ could satisfy the conditions of such a prophecy. A. F. Muir, in The Pulpit Commentary on Jeremiah 2:28.
However, when one reads Hebrews without the modern church in mind, the book 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. Here I am following Richard Hays (“We Have No Lasting City,” pages 151-173 in The Epistle to the Hebrews and Christian Theology, Grand Rapids: Eerdmans, 2009). Hays looks back at his work on Hebrews which indicates the book is supersessionist, but he then shows how a proper reading of Hebrews will show the book is not actually teaching the Christian Church has replaced Israel.
In fact, to put the question this way is a modern theological question which Hebrews does not really address. The writer is interested in demonstrating a proper understanding of the Hebrew Bible in the light of Jesus’ work on the cross will result in Christian faith. And that faith, according to the writer of Hebrews, is a kind of natural development out of Judaism to something new and different.
Although this is similar to Paul (the church is not new Israel but something new entirely), the problem of the status of the Gentile in the present age is absent from the book of Hebrews. Although this is a common theme in the Pauline letters, is entirely absent in this book since the writer is concerned with the status of Jewish believers in Christ.