It may well be that Psalm 21 is a companion to Psalm 20. Psalm 20:4 requests God grant the “desires of your heart” and Psalm 21 says that God has granted them.
In any case, Psalm 21 is a prayer on behalf of the King.
Verse 8 pairs the Lord and the King in the work of destroying the wicked, and we wonder how much relevance such a Psalm can have today.
Ancient Israel lived in a theocracy where God was the true sovereign for the nation and the king his servant. The United States is no such theocracy. And yet, we should not be quick to dismiss the relevance of this Psalm. God is still sovereign over all nations. Our leaders, whether they be Christians or not, respectful of God or not, are still servants of God (Romans 13:4). Their task is still to bring punishment on the wrongdoer that we (God’s people) might live “quiet and peaceful lives in all godliness and holiness” (1 Timothy 2:2). And our duty is still to pray for them.