I want to paint a brand new oak door it with a clear varnish to keep the grain of the timber visible. what sort of primer should I use?

If you want to see the wood grain you never use a primer. You may wish to use a stain (light oak, medium oak, or dark oak stain probably) to bring out the grain and then top it off w a varnish.

You don't use primer under varnish, but it's probably a good idea to use a sanding sealer. Make sure you use one that is compatible with your varnish.

A varnish soaks into the wood. Primer would prevent it from doing that.

Update;

I was wrong about the primer... (a little thought lapse)

Sorry

You would not use a primer on that at all.

I would stain the door first and then apply the clear coat. There are various color stains that you can use. If you want to keep the natural color of the wood then you can use "natural" stain. Or you can use one of the darker stains.

Sand it first. You might want to use a color stain after that depending upon how you want it. Then use a clear coat. They will give you pointers at the hardware store.

You don't prime for varnish.