Yes, if they're a named driver on your policy or they're covered for driving other cars by their insurance policy. They'll need to check their insurance certificate to see if they have this and they may only be covered on a third party basis.
If you'd like to add someone as a named driver, you can do this online:
If you have a car policy, you can add a driver in MyAccount or the app
If you have a bike or van policy, go to the online form and select 'add a driver'
You'll be given a quote for the change, which will include any difference to the price of your policy and any applicable fees.