From Beale’s book A New Testament Biblical Theology:
..God had designed that the nation of Israel be a corporate national Adam who was to represent what true humanity should be like (see, e.g., Deut. 4:6-8). Unfortunately, Israel proved to be unfaithful just like Adam.
This discussion has significance for understanding what it means for the predominantly gentile church to be seen as the continuation of true Israel. It means that being identified with true Israel is neither a narrow parochial identification nor one that erases gentile identity. Rather, the church is also identified with what it means to be true Adam, especially in its identification with Jesus, the true Israel and last Adam. Consequently, for the church to be the beginning of true end-time Israel is to begin to be identified with the original purposes of Adam, true humanity, which Christ has fulfilled.
Therefore, it is important to maintain that the church is not merely like Israel but actually Israel. This is most in keeping with the original purposes of Israel itself and why the OT prophesies that in the eschaton gentiles become a part of Israel and not merely be redeemed people who retain the name “gentiles” and coexist alongside but as a separate people from redeemed ethnic Israel. These OT prophecies did not envision that gentile converts to Israel would have their complete gentile identity erased, but neither did these prophecies foresee that redeemed gentiles would exist alongside as a separate people but separate from redeemed Israelites. Rather, these converted gentiles would come to be identified with Israel and Israel’s God. Such eschatologically converted gentiles would become identified with Israel as had gentiles in the past, such as Rahab, Ruth, and Uriah. Their gentile identity was not eradicated, but they came to have a greater identity as true Israelites.
The one difference, however, between converted gentiles of the past and those in the future eschaton, which is revealed more clearly in the NT (e.g., Eph. 2:12, 19; 3:4-6), is that the latter did not have to move to geographical Israel, be circumcised and worship at the temple, obey the food laws and observe the holy days, and follow other laws distinguishing national Israel from the nations. Rather, in the end-time period gentiles identify with Jesus, true Israel, and become part of the temple in him and are circumcised by his death and are made clean in him. In the new age, Jesus, as true Adam/Israel, is the only identification tag that transcends gentile identification marks or the old nationalistic Israelite identifying marks of the law.
…What is the essence of the “mystery” in Eph. 3? It was not clear in the OT that when Messiah came, the theocracy would be so completely reconstituted that it would continue only as the new organism of the Messiah (Jesus), the true Israel. In him Jews and gentiles would be fused together on a footing of complete equality through their corporate identification.*
G.K. Beale, A New Testament Biblical Theology: The Unfolding Of The Old Testament In The New (Grand Rapids: Baker Academic, 2011), p.653-654