In the Kingdom, who will sit on the throne in earthly Jerusalem? Will it be Jesus or David? As I understand it, God will be present in Jerusalem, but also in the New Jerusalem where the Church will live, as will Jesus. Who will be charged with day-to-day governance of the natural humans in Israel — who will be the “cops”?
And, in the rest of the world — the believing Gentile survivors — who will run things? Does the Bible address this, or are these more of the things we are not told about and will simply have to wait to see what develops?
When He comes back, the Lord will be King of the whole Earth (Zech. 14:9) and will occupy David’s throne (Luke 1:32-33). There will be someone called “the Prince” who seems to be in charge in Israel (Ezek. 44:3), although God the Father will have His Throne there as well (Ezek. 43:7). The Prince will be a human in his natural state. We know this because he’ll offer sacrifices for his own sins (Ezek. 45:22) and have children (Ezek. 46:16). Beyond that, the Bible is silent.
The Gentile nations will be governed by kings (Rev. 21:24) although it’s not clear who they’ll be. Since Jesus is the King of Kings, all who govern on Earth will report to Him. The Bible is also silent concerning how the nations will be administered, so we’ll just have to wait and see.