The writer returned to his former thought of all creation being under God's authority (vv. 4-5). He now summoned all creation to praise God at the prospect of His righteous rule. Verse 13 is one of the clearest and most thrilling revelations that God will rule on the earth, not just from heaven. He will do so in the person of His Son when He returns to earth. He came the first time to save the world. He will come the second time to judge it. Therefore all creation may rejoice. Even the world of plants and animals with benefit from His righteous rule (cf. Rom. 8:20-22).
This favorite psalm glories in the righteous Sovereign of the universe. His kingdom will indeed come. He will one day accomplish His will on earth as today others carry it out in heaven (Matt. 6:10).