There are two possibilities to this question.

One, since God is going to return our earth to its original state, the pre-sin Garden of Eden condition, the answer to the question focuses on the rotation of the earth.  

The earth always rotated around the sun, meaning there was night and day. The rotation of the earth did not occur because of sin or the flood. So if the Earth will continue to rotate as it always has, then there will be sunsets.

On the other hand, the Bible says heaven is illuminated by God.

The city does not need the sun or the moon to shine on it, for the glory of God gives it light, and the Lamb is its lamp. Revelation 21:23 

There will be no more night. They will not need the light of a lamp or the light of the sun, for the Lord God will give them light. And they will reign for ever and ever. Revelation 22:5

So if the earth is constantly illuminated, then there will be no sunsets. But, how can a round earth be evenly illuminated on all sides by a single light source?

The second possibility here is the difference between the new heaven and the new earth.  Maybe the new heaven (the new Jerusalem or the heavenly city where God dwells) is illuminated by God around the clock, while the new earth continues to rotate around it.

God created some animals to live in darkness (nocturnal) so what happens to them?  Does God re-create them to live in light?

Heaven, where God dwells, could act as the “sun” and the earth still spins on its axis around it, causing sunsets and sunrises to occur from the earth’s perspective.

Then again, God can do anything he wants and if he wants sunsets, there will be sunsets.

If there are sunsets, then there would be sunrises too, one of the prettiest times of the day we know.  In heaven, God will be the most beautiful thing we have ever seen so those things today are only glimpses into his beauty then.