Albert Barnes Commentary Psalms 37:6

"And he will make thy righteousness to go forth as the light, And thy justice as the noon-day." — Psalms 37:6 (ASV)

And he shall bring forth your righteousness as the light - This means that if you are slandered, if your character is assailed and seems to you to be under a cloud, or if reproach comes upon you from the schemes of wicked people in a way that you cannot counter it—then, if you commit your case to God, he will protect your character. He will cause the clouds to disperse, and everything concerning your character and the motives of your conduct will become as clear as the sun without a cloud.

There are many situations in which a man cannot counter the assaults made on his reputation. He may be unable to trace a slanderous accusation to its source or immediately explain the circumstances that lend the slanderous report an appearance of plausibility, even while he is perfectly conscious of his innocence.

In such cases, his only recourse is to commit the whole matter to God. Indeed, there is nothing that can be more safely left with him, and nothing that God will more certainly protect than the injured reputation of a good man.

Under his administration, things will ultimately work out correctly, and a man will have all the reputation he deserves. But he who spends his life merely defending himself will soon have a reputation hardly worth defending.

The true way for a man is to do his duty—to always do right—and then commit everything to God.

And your judgment - Your just sentence. This means God will ensure justice is done to your character.

As the noon-day - The original word here is in the dual form and properly means “double-light;” that is, the strongest, brightest light. It means “noon” because the light is then most clear and bright. The idea is that he will make your character perfectly clear and bright. No cloud will remain on it.