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.
You can reduce payments by offering a voluntary excess, but keep in mind not to offer a huge sum as you will need to meet it if you make a claim that is your fault. many think they will never make a mistake and it will only be someone else, but statistics shows otherwise.
Voluntary excess is an agreement you make with the policy provider to pay a higher percentage of excess at the time of an insurance claim. This also means it would be unlikely you would make a claim for a small amount of cash and risk losing your no claims bonus.