A key idea in the Bible is that God chose (‘elected’) people to serve his purposes for the world. First he chose Abraham (Gen. 12: 2) and the nation that sprang from him rather than any other nations, even though they were mightier or more numerous than Israel (Deut. 7: 7). It was a matter of God's free, almost arbitrary, decision—but repeatedly Israel failed, by idolatry or disobedience, and Isaiah prophesied that only a remnant of the nation would survive to reap the rewards of faithfulness when God's day of judgement came (Isa. 37: 31 ff.). So the original assumption that the whole nation was elected was gradually scaled down.
The NT represents the climax of this process, in claiming that finally God chose a single individual alone to fulfil his purposes for mankind—Jesus. When that had been accomplished, then the company of the elect could begin to expand again, and ‘a chosen race, God's own people’ (1 Pet. 2: 9; the Christian Church) replaced the old as the object of God's election and the inheritors of his promises (Rom. 4: 9 ff.). In effect, the Church is the New Israel, though that term is not used in the NT.
As with old Israel, the Church's privileges are complemented by responsibilities; they are to proclaim God's mighty acts (1 Pet. 2: 9) and those who are chosen will respond to the preaching (1 Cor. 1: 24). Paul insists that salvation is entirely the work of God (1 Cor. 1: 30 f.), giving the believers a sense that they need not fear the day of judgement (Rom. 8: 33 ff.), and this conviction is the incentive towards a holy life (Col. 3: 12 f.). The Gentile response to God's election will be so substantial that, Paul maintains, the Jews will also be won over to faith in Christ (Rom. 11: 2, 28).