How do I make a Custom Player Icon in the Leaderboard? I.e: A Star instead of a Ribbon as Owner.

I haven't tried because I couldn't figure it out but I did try the game:GetService('StarterGui'):SetCore, But I could figure that out from there. How do I do this?

Well, you can't edit the player list/leader board from scripts. If you use a custom leader board you could do it. But unfortunately ROBLOX does not let us edit those parts of the core.