The Book of Revelation chapter 21 verse 1 answers your question when it says: "and I saw a new heavens and a new earth." The implication here is we simply enter into a new cycle or round of Creation as a result of God the Father establishing His Kingdom in victory.
This comes into focus clearly when you understand how to decipher the Creation Account as the master blueprint for the Creation itself in order to reveal the hidden mysteries. In order to do so you take each Day of Creation as pertaining to a distinct Millennium of Creation. This means that one round or cycle of Creation has a duration of approximately 7 thousand years and that we are in the process of entering into the 7th Day of Creation, which is the Millennium when Christ rules and reigns in a period of rest from the Adversary.
Obviously there are implications in what I have said that many people will not find comfortable to contemplate. The biggest is that the Days of Creation are not directly speaking about the creation of our physical observable cosmos.
For example, if you look at Day 4 when the "greater light to rule the day" is being spoken of, you would need to interpret this as Jesus Christ, the light and life of the world who came in the 4th millennium instead of the creation of our physical sun that shines light for us day in and day out.
As another example, look at Day 5 where it speaks of the "creatures in the waters wherein dwells the breath of life". This is the part of the master blueprint calling for the ministry of the apostles to be "fishers of men" and to gather them into the body of Christianity as a new religion to begin the next level of this cycle of Creation's evolutionary stage of spiritual development. This is why Christian's put little fish symbols on their cars. It was right in the beginning of the 5th Millennium that Christianity was established, which is right on schedule according to the master blueprint.
So, just like we pass from Sunday to Monday to Tuesday to Wednesday to Thursday to Friday to Saturday and back to Sunday again, so too does the geo-geneo-political framework of things on our planet cycle through millennia such that a single cycle of Creation is like a week that repeats over and over again.
However, there is a difference that should be noted: The 7th Day is simultaneously the 1st Day as well. One cycle of Creation overlaps the adjacent cycle of Creation. This gives us the Alpha/Omega Millennial period. There are many hints to this in scripture I could elaborate upon if desired.
So, while we are looking for the Millennial Rest under Christ as King of the Father's Kingdom on Millennial Day 7, we should also be anticipating a period of great darkness and chaos preceding this because we are also approaching a new Day 1 as well. We know that prior to a new Creation's Day 1 that there is a period of darkness and chaos. This is in a geo-political sense, mind you.
So, it is the Father's Kingdom that is spoken of in Day 1 where it says the light breaks fourth putting an end to the darkness and chaos such that those of the dark are divided. This is the judgment or separation aspect that takes place during the Millennium. Those who have eyes to see and ears to hear will embrace the light of the Father's Kingdom and attain to their spiritual birth (resurrection) while all else shall remain in darkness blinded by the precepts of men. These are those who draw near unto God with their lips but whose hearts are far from Him, having the form of Godliness but who deny the powers thereof and govern themselves via the commandments of men.
In their blindness they suffer themselves to continue to practice a dead religion that leaves them bound to the Adversary's cunning deceptions as his "prison planet" system takes captive all those who reject the light and truth of the Father's Kingdom. While on the other hand those who do recognize and accept the light and truth of the Father's Kingdom and join themselves to it by covenant shall be permitted to live in that Millennial society the Adversary loses all power over.
The gulf of separation between those of the Father's Kingdom and those of the Adversary's Kingdom will become impassable. Those who the Adversary takes captive will loose all of their freedom to choose and will become mere subjects of a tyrannical state. Many will champion this as the answer to the world's problems and will be deceived into building this system of governance up and fall into the very pit they helped dig for others.
On the other hand, those in the Father's Kingdom will escape the clutches of this tyrannical system of governance and they will participate in what will appear like America rebooted, except it will be a Kingdom of kings instead of a republic of sovereigns. It will be the re-establishment of liberty where total respect will be renewed for the unalienable rights granted by our Creator.