‘The differences between the church and Israel are rooted in the newness of the covenant by which God and his people are bound to each other. The new covenant under which the church lives (1 Cor 11:25 Heb 8:7-13) is a new form of the relationship whereby God says to a chosen community, “I will be your God; you shall be my people.” (Ex 6:7 Jer 31:33) Both the continuity and the discontinuity between Israel and the church reflect this change in the form of the covenant, which took place at Christ’s coming.
The new features of the new covenant are as follows:
First, the Old Testament priests, sacrifices, and sanctuary are superseded by the mediation of Jesus, the crucified, risen, and reigning God-man (Heb. 1-10), in whom believers now find their identity as the seed of Abraham and the people of God. (Gal 3:29 1 Pet 2:4-10)
Second, the ethnic exclusivism of the old covenant (Deut 7:6 Ps 147:19-20) is replaced by the inclusion in Christ on equal terms of believers from all nations. (Eph 2-3 Rev 5:9-10)
Third, the Spirit is poured out both on each Christian and on the church, so that fellowship with Christ, (1Jo 1:3) ministry from Christ, (Jn 12:32 14:18 Eph 2:17) and foretastes of heaven (2 Cor 1:22 Eph 1:14) become realities of churchly experience.’
(J.I. Packer, Concise Theology)