First off, the heading. A Benjamite named Cush isn’t mentioned in the Bible. Maybe he was involved in one of the rebellions, or loyal to Saul? Maybe it’s a different name for Saul?
Psalm 7 has similar content to Psalm 6 (protecting from enemies), but the focus is significantly different. Psalm 6 has confession of guilt, but Psalm 7 talks of protesting innocence before people. David can do this because we see through the Psalm that God is a god of justice, and he will bring about justice. Paul, for example, speaks the same way in 2 Thessalonians 1:6-7. I think of Haman reaping what he sowed (Esther 7). And so this moves us to thank God for his justice (5:18)!
I think of how David had not done harm to Saul’s family, as was common when nations switched dynasties. David passed up chance after chance to kill Saul (1 Samuel 24, 26), he praised the people who buried Saul and Jonathan (2 Samuel 2:4-5), he punished those who murdered Ish-Bosheth (2 Samuel 4), and he welcomed and befriended Mephibosheth (2 Samuel 9). I mean, look at 7:5. David is saying it’s wrong to plunder your enemy for no good reason.
Oh, and one grammar thing. The Hebrew switches from singular to plural for David’s enemies, while English translations smooth it out, which is fine. Just something to note, Hebrew writers weren’t so worried about such syntactical details.