UAE registered car in Saudi Arabia, how do I get it insured

Not clear what you are asking exactly.

But you can get a full "GCC cover" from your UAE insurance provider and when you bring the car to Saudi, you can buy third party insurance cover at the border.  GCC cover will only take care of damage to your car in Saudi but not indemnify against third party loss - which is why separate cover is needed.

Many thanks, this is exactly what I was looking for.  However, both Oman Insurance and AXA Insurance in the UAE say that they do not provide GCC wide insurance cover, do you know of any car insurance company in the UAE who can provide the insurance cover?

I used to have it with RSA.  Get an insurance broker who can suggest you options - no cost to you.