If you cant relocate the tank while you paint, then covering it is the enxt best option. I'd turn off any airstones etc. just in case - just leave the filter running.
If you're setting up a new tank from scratch, you'll need to condition the water.
Can you use your old filter in the new tank (to trasfer the nitrifying) bacteria? or is it a sealed & fixed system.
If you cant use the old filter in the new tank, you'll need to cycle the new set-up before adding fish.
You can look up methods for fishless cycling in the pinned topics in the beginner section