Many of David's Psalms were written about his conquests in battle and how God is the One who gave him victory. Many of them also find their ultimate meaning in our Lord Jesus Christ. The writers of the New Testament saw Christ in all of the Old Testament.
I see that here in Psalm 21 as it describes how Christ's enemies will come to an end as He displays His wrath against the wicked.
8 Your hand will capture all your enemies; your right hand will seize those who hate you. 9 You will make them [burn] like a fiery furnace when you appear; the Lord will engulf them in His wrath and fire will devour them. 10 You will wipe their descendants from the earth and their offspring from the human race.
David's response should be our response.
13 Be exalted, Lord, in Your strength; we will sing and praise Your might.
You'll find "I will sing" this or that all through the Psalms (they are songs after all) but this one says "we will sing and praise Your might." It's a good reminder that not all of our faith and our expressions of faith are not meant to be isolated, by-ourselves events. There is a place, of course, for private worship - a very important place. But there is an equally important place for corporate worship - worshipping together with other believers.
It's so important that the writer of Hebrews said it this way -
23 Let us hold fast the confession of our hope without wavering, for He who promised is faithful ; 24 and let us consider how to stimulate one another to love and good deeds, 25 not forsaking our own assembling together, as is the habit of some, but encouraging one another; and all the more as you see the day drawing near.