With regards to the rest of the Psalm, there are two explanations when it comes to the main character (he/He). Is it about the (earthly) king or is it about God the Lord? I choose the Lord as an agent. It is not a problem to choose the (earthly) king as the main character. All his actions, his deeds, he has received from the Lord God.
Again, we have two parallel sentences. Your hand is the right hand, that of power. And an enemy is someone who hates the king or God.
Your hand will strike (find
) your enemies. It is a euphemism for the fact that the Lord will defeat his enemies. There is no escape from it. He gets hold of the haters and thus the king is saved (see Psalm 21:1 and Psalm 21:5 salvation
). Because of the mighty hand of the Lord, the king does not waver (Psalm 21:7).
8 Your hand will find out all your enemies; your right hand will find out those who hate you.