Polyurethane is a category of wood finish products that are either water- or solvent-based clear coatings that can range from a gloss finish to a satin finish. Under most circumstances, a varnish product can be applied over a polyurethane coating. It is very important to test in a small, inconspicuous spot to see if the varnish achieves the desired result, and forms proper adhesion to the polyurethane.
It is extremely important that the polyurethane product has completely cured for at least 5-7 days. After that time, lightly scuff sand, then remove any sanding residue prior to applying the varnish product.