This quotes Psalm 32:1-2:

1 Blessed is he whose transgression is] forgiven, whose sin is covered. 2 Blessed is the man unto whom the LORD imputeth not iniquity, and in whose spirit there is no guile.

The New Testament teaching of salvation does not contradict the Old Testament teaching of salvation.  One could and should argue that the gospel of the New Testament proceeds from the Old Testament.  “New Testament” doesn’t mean “new” as in, never seen before, of very recent origination.When Jesus describes salvation in His Sermon on the Mount, He describes the ultimate fulfillment as “blessed” in what we call the beatitudes.  These correspond to the blessings promised in the Old Testament, including in the psalms, and David starts Psalms 32 with “Blessed.”  For man to be saved, which is to be blessed, he needs atonement for or removal of his sin.  He might try to do good and David already wrote in Psalm 14, that is hopeless.Later Paul argues in Romans 4 from Psalm 32 that David was trusting the Lord for his salvation, not in his own works.  I always like to say, works can’t get rid of your sin, even if you did them.  If you really determined to be good from now on, to be saved, you still need the cleansing of the past sins.  While you’re attempting to do good works, you are still failing, so you also need those sins taken away.  Salvation by necessity requires what David describes in Psalm 32.Psalm 32 is most known as David’s confession of his sin, adultery with Bathsheba and murder of Uriah.  The first two verses though are not a confession.  They are, however, a prerequisite for confession.  First comes conversion, then comes confession.  In 1 John 1 and 2, the Apostle John communicates that we don’t hide our sin because we do have cleansing and propitiation.  The sins aren’t forgiven because of confession. They are forgiven because of the salvation that is the basis of the confession.The experience of blessing doesn’t come from confessing sin.  It comes from a believer confessing sin.  An unbeliever could confess sin, but he will not receive forgiveness, covering, or imputation of righteousness for mere confession.  Confession is a lifestyle or a habit of a believer, because he receives forgiveness of sin by grace through faith as a prerequisite for confession.Three terms designate the dimensions of human evil:  transgression—acts reflecting rebellion against God, sin—the most general term, designating an offense, or turning away from the true path, and iniquity—indicating distortion, criminality, or the absence of respect for the divine will.  In the context, the three terms should not be viewed per se as pointing out just three specific kind of sins, but taking all three as a whole to specify the full dimensions of human evil from which someone requires deliverance.  It’s too overwhelming to dig himself out of it through confession.The person’s spirit has no guile, because he is truly repentant.  This is not a game that he’s playing, showing up to his confessional booth week after week.  He can’t confess as a means of experiencing the blessing and forgiveness without a spirit that has already been changed.  He doesn’t like his sin.  He doesn’t mean to keep sinning.When one arrives at the end of the psalm in verse 10-11, David writes:

David contrasts the wicked with “he that trusteth in the LORD.”  Mercy compasses him.  From this mercy proceeds gladness, rejoicing, and shouts of joy, not because of what he has done, but because of what God has.Psalm 33 begins like Paul in Philippians 3, when he describes his own salvation:  “Rejoice in the Lord.”  Paul may have been quoting Psalm 33.  Habbakuk later writes (3:18):  “Yet I will rejoice in the LORD, I will joy in the God of my salvation.”  He relates joy to the salvation of God.  With the Apostle Paul, rejoicing in the Lord meant not boasting in himself and putting confidence in his flesh, counting as dung and loss all things that he might win Christ.The psalm ends with these verses:

The king is not saved by his own strength of that of a horse, but through the fear of the LORD and hope in his mercy.  He waits on the LORD for his help, rejoices in Him, trusting in His holy name.Similar to Psalm 32:1-2, David writes in Psalm 34:8, “blessed is the man that trusteth in [the LORD].”  In the end of that psalm, he says in vv. 18 and 22:

18 The LORD is nigh unto them that are of a broken heart; and saveth such as be of a contrite spirit.  22 The LORD redeemeth the soul of his servants: and none of them that trust in him shall be desolate.

Here are the components of a salvific response to God.  God does the saving, and He saves those of a broken heart, a contrite spirit.  He redeems their souls and when they trust in Him, they will not be desolate.Trusting God means not trusting one’s own self.  The Lord redeeming means his not redeeming himself.  The offering that God accepts is not his own works, but as David writes in Psalm 51:17:

The sacrifices of God are a broken spirit: a broken and a contrite heart, O God, thou wilt not despise.

This is the soul that God will redeem, the one offered to Him, broken and contrite.  He can though depend on God for salvation.  “O taste and see that the LORD is good” (Psalm 34:8).