You can call it a promise, you can call it a prophecy, but Psalm 37 indeed is perspective on how God deals with the wicked in history, and how the righteous should react to evil plans which we often see in history.

Psalm 37 is very much a part of Revelation’s view
of the plans of evil men.

It does view sinful inclinations of men as producing evil plans that are often of monstrous proportions. Revelation concentrates on two principal covert actors in history: Mystery Babylon the Great, and the beast organization (called the mystery of Lawlessness in 2Thessalonians chapter two).

The other side of these things is that such things are often seen and recognized as evil in history. Through crafty manipulation and covert action, great fortunes and power are often amassed in history. Evil men often dominate nations and even continents, and they care nothing about whether they ruin, or hurt or slaughter the innocent. These are continual things in history. Those trying to do what is right are often exasperated by these things, but such things are outside of their power or influence. Should we envy such power and wealth, and seek it ourselves?

What should be the perspective of the
men and women of God?

The theme is announced in the first four verses.

“1 Don’t fret because of evil-doers,
Neither be envious against those who work unrighteousness.
2 For they shall soon be cut down like the grass,
And wither like the green herb.
3 Trust in Yahweh, and do good.
Dwell in the land, and enjoy safe pasture.
4 Also delight yourself in Yahweh,
And he will give you the desires of your heart.”
Psa 37:1-3 WEB

It continues along such a line for a full forty verses. Should we fear them? Center our lives around opposing them?

“7 Rest in Yahweh, and wait patiently for him.
Don’t fret because of him who prospers in his way,
Because of the man who makes wicked plots happen.
8 Cease from anger, and forsake wrath.
Don’t fret, it leads only to evildoing.
9 For evildoers shall be cut off,
But those who wait for Yahweh shall inherit the land.
10 For yet a little while, and the wicked will be no more.
Yes, though you look for his place, he isn’t there.”
Psa 37:7-10 WEB

All of this life, and ALL of human history is but a little while. This is really advice to those caught in such times, and in the violent storms which will surround the end of life in this universe as pictured in the book of Revelation. It is a commentary and a reminder on on,

“God resists the proud, but gives grace to the humble.”
1Pe 5:5

“28 For Yahweh loves justice,
And doesn’t forsake his saints.
They are preserved forever,
But the children of the wicked shall be cut off.
29 The righteous shall inherit the land,
And live in it forever.”
Psa 37:28-29 WEB

It is talking about heaven, the new heavens and the new earth of Revelation 21 and all the rest.

WEB is the World English Bible, a copyright free revision
of the original ASV American Standard Version 1901