12 But as many as received Him, to them He gave the right to become children of God, even to those who believe in His name, 13who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
Jesus promised us to become children of God, born of God.
1 Peter 1 echos this sentiment:
For you have been born again, not of perishable seed, but of imperishable, through the living and enduring word of God.
2 Peter 1 reminds the reader of the same:
4 by which he has granted to us his precious and very great promises, so that through them you may become partakers of the divine nature, having escaped from the corruption that is in the world because of sinful desire.
Ephesians 1 spells out the promised Holy Spirit:
13 And you also were included in Christ when you heard the message of truth, the gospel of your salvation. When you believed, you were marked in him with a seal, the promised Holy Spirit, 14who is a deposit guaranteeing our inheritance until the redemption of those who are God’s possession—to the praise of his glory.
These are the promises: The Holy Spirit lives in us. We become children of God. We take on the divine nature of eternal life.
Ellicott makes an important point concerning the Greek word promise:
The Greek word occurs here and in 2Peter 3:13 only. Its termination indicates the things promised rather than the act of promising. They are "exceeding great," or rather "the greatest," because they contain an earnest of the completion and perfection of the Christian life; they are very "precious," because this earnest is in itself something real, and not mere empty words. Not the promises of the Old Testament are meant, that Christ should come; but those of the New Testament, that Christ should come again. The certainty of Christ's return to reward the righteous and punish the wicked is one of the main subjects of the Epistle.
The OT promises are mostly types of the true types in the NT.