For a glued layer, apply a bonding agent. For an unbonded overlay, add your interlayer so that the top surface is level. The simple answer is YES, new concrete can be poured over existing concrete. If you can pour new concrete over old concrete, you probably want to know the risks you would take in doing so.
If you simply pour new concrete on it and it doesn't fix the problem, the same thing will most likely happen to new concrete. If you ripped out old concrete and replaced it with new, well-poured concrete, you could save yourself a lot of trouble by maximizing the life of your concrete. Yes, you can put new concrete on top of old concrete as long as there are no problems such as significant cracks or frost elevations with existing concrete. When existing concrete is severely damaged, with large cracks going through the structure, you need to completely tear it off and replace it.
Finish the work by priming the surface and pouring a mixture onto it, giving your concrete base a fresh new layer. Technically, existing concrete could be covered with a layer of concrete only a few millimeters thick, which is called a screed. Alternatively, do some research on concrete-safe chemicals that help lift the paint so you can scrape it off. You can stamp concrete as mentioned above, but you can also color it, dye it, engrave it, or even use stencils.
If the concrete doesn't move, move, or settle, then it's OK to pour new concrete on top. If you don't do everything you can to avoid it, you may be replacing the concrete sooner than you'd like. Fresh concrete does not adhere well to existing dry concrete because it does not contain any natural bonding agent. Heavy concrete, of course, will use heavier rebar, but smaller concrete, such as the sidewalk or driveway, will only require about half an inch of rebar.
While pavers, stones and other types of paving materials offer a more decorative look, concrete is valued for its strength and low maintenance.