If you are buying a second car, your no claims discount may only apply to your first car, but you may still get a lower car insurance quote if you have not made a claim previously and use that car insurance company for your first car.
Having car insurance is a legal requirement to drive on the UK public roads. The minimum cover you can buy is Third Party, but some insurers won't sell you this cover on its own as it does not cover the insurer in cases where the car is stolen or where the fault lies with the insurer. It may also be the case with learner driver first alternative car insurance.
Always read the small print on your car insurance policy to see just what is and isn't covered.If you are unsure about anything ask! Idealy before you buy your next learner driver first alternative car insurance policy, they are there to help you.
If you were buying a new car you wouldn't buy the first car you see. Car insurance is no different you can save hundreds of pounds by shopping around.