Varnish is a pain to paint over. It needs a lot of sanding. Often so much that you will invariably end up sanding through the varnish and hitting the wood. Hence the need for primer.
Unfortunately, in many cases, once you apply the first undercoat you will notice bucket loads of dents that were not visible when the door was varnished. For that reason, I sand away all of the varnish. Once the wood is a uniform colour, I know that it is dent free.
I have no idea if you are planning to use oil or waterbased paints but you can buy waterbased (acrylic) primer/undercoat in grey.
Alternatively, if you only want to buy one product this
may be suitable as a primer/undercoat/top coat
https://www.toolstation.com/bedec-multi-surface-paint/p36878
I have never used it and caution you that all waterbased paints will cause the grain to raise (requiring you to sand it back as you go).