You have fully comp car insurance can idrive another persons car third party if the car has a current mot and tax but the owners insurance has runout?

Of course you can drive it... you can drive any car you want... I think the question you are asking though is whether or not it will be legal to drive and whether or not an out of force car insurance policy will cover you if you wreck the vehicle even if it has a current tax and license... right?

The answer to those questions is NO. If the current owner's coverage is not in force, it is not legal for you to drive the vehicle unless you have a Non-Owner Insurance policy which insures any vehicle you drive.

An out of force policy will NOT cover you at all.

Whether the vehicle has current license and tax has no bearing at all on whether you meet your States insurance guidelines.