The future tense of the verb (“will save”) is not a denial that salvation is also a present aspect of Christian existence (cf. 1:15; 2 Tim 1:9); rather, Paul envisions the potential influence that Timothy’s life and teaching hold both for his own and the church’s greater realization of God’s salvation. Tying the fortunes of these two parties together is also Pauline (1 Cor 10:33; 9:22); as Paul’s delegate, Timothy exists to serve others, and his realization of the fullness of salvation is incumbent upon a faithfulness that stretches from personal character to the quality of his teaching and service to others.
Thus salvation through Christ, as mediated by the gospel and “the teaching” to “those who hear” responsively, is a present reality.
Philip H. Towner, The Letters to Timothy and Titus, The New International Commentary on the New Testament (Grand Rapids, MI: Wm. B. Eerdmans Publishing Co., 2006), 328.