The Bible tells of how God has selected for himself a people through which he will accomplish special purposes within his mission of redemption and recreation. This mission of God's people is the central way in which they participtate in the Mission of God.
There is one people of God, but the church does not replace Israel. Continuity and discontinuity exist between the Old Testament people of God and the New Testament people of God. Though, the church does not replace Israel. While this may seem tangential to the question of mission, it is an important aspect of developing a theology of mission for the church. If the church merely replaces Israel, then the church takes on all of Israel's purposes as well as any added to it by the New Testament. There is a tendency today to overload an understanding of mission with every imperative found in Scripture that is directed at a people of God. While all Scripture is essential for doctrine and instruction (2 Timothy 3:16), that does not mean that a wholesale transfer of God's purposes for the Old Covenant are proper in developing the mission of the church. The Old Covenant finds it's telos in the person and work of Christ, the true Israel.
The Church as God's New Covenant Community
The church is, in fact, a New Covenant people who are not under the prior covenants. As noted by Gentry and Wellum:
However, the fact that Christ has fulfilled the previous covenants does not entail that the earlier covenants have no value for us today or that we can jettison the Old Testament from our Bibles. After all, the previous covenants serve their role in God’s redemptive plan and revelation of himself; they are forever part of Scripture, which is for our instruction, growth, and ministry (2 Tim. 3:16–17). Yet, now that Christ has come, Christians are no longer under these previous covenants as covenants. A crucial implication of this point is that we, as new covenant believers, must view and apply the previous biblical covenants to ourselves in light of Christ, to whom each of the previous covenants pointed and who fulfills every aspect of them completely. This observation is crucial in discerning how the previous covenants “carry over” to Christians in regard to our lives. God's Kingdom through God's Covenant (Gentry & Wellum, 2015), 254.
Thus, without creating too much discontinuity between the Old Testament people of God and the New Testament people of God, it is necessary to see the newness of the New Covenant. The Mission of the Church comes at a particular place in God's unfolding promise place, and fulfills a unique aspect of the overall mission of God.