The Bible says very little about what will happen at the end of the 1000 year reign of Christ. In fact, there are probably only two relevant passages: Revelation 20:7-15 which describes a final battle and final judgement, and 1 Corinthians 15:24-28 which says
Then comes the end, when he [Christ] delivers the kingdom to God the Father after destroying every rule and every authority and power. For he must reign until he has put all his enemies under his feet. The last enemy to be destroyed is death. For “God has put all things in subjection under his feet.” But when it says, “all things are put in subjection,” it is plain that he is excepted who put all things in subjection under him. When all things are subjected to him, then the Son himself will also be subjected to him who put all things in subjection under him, that God may be all in all.
Neither of these passages describes what happens next.
There are Bible passages which describe a “new heavens and a new earth” (e.g., Isaiah 65:17; 66:22; 2 Peter 3:13) but these seem to describe the time when Jesus returns and refer to a new world order rather than literally a new planet.