Acts 10:43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
While Peter spoke these words to the assembled Gentiles at Cornelius’ house, the Holy Spirit was seen to fall on them. This ”Gentile Pentecost” convinced Peter and his group that Jesus died snd rose to bring forgiveness to all people. And this is God’s promise to us as well: all those who believe in Jesus will receive remission of sins through His name.
The promise of forgiveness is unconditionally granted to all people by grace. But faith in Jesus is the condition that makes it personal and real. And such saving faith is a gift given by the Spirit through the Gospel. When the gospel is preached faith in the name of Jesus is worked in the hearer, and he receives the promised forgiveness of sins.
When sins are truly forgiven and cleaned out of the inner spirit of a man the Holy Spirit moves in to dwell with the eternal life of God. Forgiveness is the negative promise: we are minus sins; the indwelling Spirit is the positive promise: we are plus a holy life. From the inner spirit the Spirit positively affects and influences the thoughts, words, and behavior of the believer. That’s the promise of the remission of sins.