Your no claims bonus will still accrue as normal. So if neither you nor your named driver has an accident, your no claims bonus will continue to build up.
However, if your named driver has an accident, it’s likely to affect your no claim bonus. That’s because, regardless of who’s driving, you’ll need to claim against your policy, meaning that the insurer provider may need to pay out.
It’s also worth bearing in mind that very few policies allow your named driver to build up a no claims bonus. This is worth considering if you’re thinking of adding a young driver to your policy, as they might not gain any no claims discount until they take out a policy in their own name. Sometimes, however, your insurance provider may offer a discount based on a young person’s driving history in your car, provided they take out their own policy with the same insurance provider.