In the NT, “faith” doesn’t greatly change meanings from the OT, except that “faith” in the NT is always faith in Jesus. Before Pentecost, the Jews believed in God and in his promised Messiah, but they did not believe in Jesus — nor were they expected to. He’d not yet been revealed.
But beginning with Peter’s sermon in Acts 2, the faith that saves becomes faith that Jesus is Messiah and Lord/faithfulness to Jesus as Messiah and Lord/trust in Jesus as Messiah and Lord.
This is anticipated by Peter’s Great Confession —
(Mat 16:15-16 ESV) 15 He said to them, “But who do you say that I am?” 16 Simon Peter replied, “You are the Christ, the Son of the living God.”
Let me rephrase this more exactly —
(Mat 16:15-16 ESV) 15 He said to them, “But who do you say that I am?” 16 Simon Peter replied, “You are the [Messiah], the Son of the living God [of Psalm 2].”
“Christ” is simply Greek for Messiah, both of which mean “Anointed One” and refer to the king promised by the OT prophets.
(Psa 2:2-7 ESV) 2 The kings of the earth set themselves, and the rulers take counsel together, against the LORD and against his Anointed, saying, 3 “Let us burst their bonds apart and cast away their cords from us.” 4 He who sits in the heavens laughs; the Lord holds them in derision. 5 Then he will speak to them in his wrath, and terrify them in his fury, saying, 6 “As for me, I have set my King on Zion, my holy hill.” 7 I will tell of the decree: The LORD said to me, “You are my Son; today I have begotten you.
Zion is the mountain on which David’s palace was built. The Anointed is also called Son of God and King — not to mention begotten of God, another way of saying God’s Son. Literally, it means “conceived by God.”
So when Peter says, “You are … the Son of the living God,” he has Psalm 2 in mind. He is saying, in a typically Jewish way, that Jesus is the Messiah in two different ways.
In Acts 2, Peter preaches,
(Act 2:22-23 ESV) “Men of Israel, hear these words: Jesus of Nazareth, a man attested to you by God with mighty works and wonders and signs that God did through him in your midst, as you yourselves know — 23 this Jesus, delivered up according to the definite plan and foreknowledge of God, you crucified and killed by the hands of lawless men.”
Peter declares that Jesus was crucified, despite being a great miracle worker.
(Act 2:24-28 ESV) 24 “God raised him up, loosing the pangs of death, because it was not possible for him to be held by it. 25 For David says concerning him, “‘I saw the Lord always before me, for he is at my right hand that I may not be shaken; 26 therefore my heart was glad, and my tongue rejoiced; my flesh also will dwell in hope. 27 For you will not abandon my soul to Hades [the realm of the dead], or let your Holy One see corruption. 28 You have made known to me the paths of life; you will make me full of gladness with your presence.”
He then says that Jesus was resurrected (v. 24) as promised by Psalm 16:8-11.
(Act 2:29-31 ESV) “Brothers, I may say to you with confidence about the patriarch David that he both died and was buried, and his tomb is with us to this day. 30 Being therefore a prophet, and knowing that God had sworn with an oath to him that he would set one of his descendants on his throne, 31 he foresaw and spoke about the resurrection of the Christ, that he was not abandoned to Hades, nor did his flesh see corruption.”
Interpreting Psalm 16, Peter points out that the psalm says that God’s servant will not be abandoned to Hades (Sheol in the Hebrew, meaning the realm of the dead — not the same thing as gehenna). But David died. Therefore, the psalmist was speaking of someone else
(Act 2:32 ESV) 32 This Jesus God raised up, and of that we all are witnesses.
Peter then says that the disciples there, 120 of them, had each seen the resurrected Jesus.
(Act 2:33-35 ESV) 33 Being therefore exalted at the right hand of God, and having received from the Father the promise of the Holy Spirit, he has poured out this that you yourselves are seeing and hearing. 34 For David did not ascend into the heavens, but he himself says, “‘The Lord said to my Lord, “Sit at my right hand, 35 until I make your enemies your footstool.”‘
Peter next argues from Psalm 110 that God promised “my Lord” that he would sit at God’s right hand. This is not David, but Jesus, who ascended to heaven to reign with God.
(Act 2:36 ESV) 36 Let all the house of Israel therefore know for certain that God has made him both Lord and Christ [Messiah], this Jesus whom you crucified.”
Peter now charges them with a very particular sin: crucifying Jesus — who is both Lord and Messiah. Obviously, not every Jew present had been involved in the crucifixion 50 days before. But the fact remained that the Jewish leaders had killed the Messiah — and now the Jewish people had to make a decision.
(Act 2:37 ESV) Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, “Brothers, what shall we do?”
Do? About what? Well, about the fact that the Messiah has come, been crucified, been resurrected, and returned to heaven to rule. And Israel had crucified him. Obviously, God could not be happy about this.
To a Jew, this also meant that the long-promised Kingdom was dawning. The Messiah had come, the Spirit had been outpoured, and it was time for the Kingdom to arrive.
But it also means that the Exile was ending and God was offering Israel the opportunity to be redeemed from Exile and to return to right relationship with him, as promised in Deu 30. And this was a promise given to the entire nation.
Therefore, hanging in the balance was God’s judgment on the entire nation of Israel. They had to repent individually, but God’s covenant was a national one — and the nation needed to make a choice.
“What shall we do?”
(Act 2:38 ESV) 38 And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit.
Repent from what? Immorality? Lying? Stealing? No, the only sin they were accused of was failing to believe that Jesus was the Messiah. Accepting Jesus as Messiah would result in their sins being forgiven — but as good Jews, the sin that most needed forgiveness was denial of Jesus as Messiah.
After all, Jesus came as a king — the King of Israel to sit on David’s throne. And for Israel to repent, they had to submit to him as King — that is, they needed to become faithful to the Messiah. You see, much more was going on than mere sin and forgiveness.
Rather, forgiveness of sin would allow God the Spirit to enter the believer — whose soul would be cleansed by God’s forgiveness.
Baptism was not controversial, although it was a fairly new practice among the Jews. The more important point is that they are to be baptized “in(to) the name of Jesus Christ.” This is a reference back to —
(Act 2:21 ESV) 21 And it shall come to pass that everyone who calls upon the name of the Lord shall be saved.
Earlier in the sermon, Peter had quoted Joel 2:32 for the principle that calling upon the name of the “Lord” (Hebrew: YHWH) will bring salvation.
Then, as quoted earlier, Peter said in Acts 2:36 that God made Jesus “both Lord and Messiah.” Well, “Lord” is a reference back to Joel 2:32. Peter is literally declaring Jesus to be YHWH. Therefore, the way Peter instructs his listeners to call on the name of the Lord is to be baptized into the name of Jesus. They had to enter the Kingdom by submitting to the King.
So that’s a very long way of stating the obvious: in the NT, “faith” is faith in Jesus. Faith in God but not Jesus of Nazareth will no longer do. You cannot be in the Kingdom if you deny the King.