The elect will be saved infallibly through the preaching of the gospel, for God determined that it would be so through the eternal covenant of redemption established among the persons of the Trinity. In his sovereign, gracious, distinguishing love, the Father has chosen certain people (Rom. 9:11-13; Eph. 1:4) whom he gave to his Son (John 6:37, 39; 17:6, 24), who, in turn, committed himself to accomplish their redemption by obeying the precepts of God’s moral law perfectly on their behalf (his active obedience) and paying the penalty due them for their disobedience to the law (his passive obedience). Thus God can be just and the justifier of those who believe in Jesus (Rom. 3:26). Under the Trinitarian covenant, the Spirit is sent into the world by the Father and the Son (John 15:26; 16:5-15) to apply Christ’s saving work to the elect...
Knowing that the elect will be gathered by the second Adam (John 17:12; Rom. 5:12-19) makes Calvinists bold in evangelism. They also are patient in it, knowing that God will save sinners in his time and way through the priestly work of Christ (Isa. 55:10-11). They are zealous, knowing that God’s glory will come to be (1 Cor. 1:27-31), and prayerful, knowing that he alone will and can accomplish salvation as an ever-faithful, covenant-keeping Lord (Eph. 2:1-10).10 Nearly all the great and zealous evangelists of the church from the sixteenth-century Reformation to the early nineteenth century, before Charles Finney (1792-1875), were committed to definite atonement rooted in this God-centred covenant theology. Would anyone dare say that George Whitefield lacked evangelistic zeal in preaching the gospel? Would anyone say the same of Charles Spurgeon, William Carey, David Brainerd, Jonathan Edwards, or Asahel Nettleton? Each of these great evangelists professed a definite design in the atoning work of Christ and boldly heralded Christ as a freely offered and willing Saviour to all who repent and believe.11
Third, while we cannot fully grasp with our finite minds how to reconcile a definite, limited atonement with Christ’s all-sufficient blood and a universal invitation to believe, such is the pattern of Scripture and the way of God (John 6:37-40). Moreover, since the atonement is not limited in itself, though it is in its design, and since the promise is that all who by faith truly come to Christ for salvation will certainly be saved (Rom. 10:13), limited atonement is not inconsistent with a universal call to faith.
https://banneroftruth.org/us/resources/articles/2009/defending-definite-atonement/