When a child obtains a learner's permit to start driving you should inform your car insurance provider of their licensing status. Many insurance companies do not require that the child be added to the policy yet, or a premium paid for them yet, but will once they start to drive on their own.
Most insurance companies do not add on a child with a permit to the policy or charge for them yet since with a permit the person is to be supervised at all times when driving. Once they move on to the next step of a state's graduated driver's licensing (GDL) program and start driving on their own they normally need to be added to the policy as a driver and then a premium for them will be charged. When the child obtains their full driver's license they clearly need to be on the policy to be properly insured.
So while most companies do not charge for a person with a learner's permit or require the learner be named on a policy, some do and thus if you have a 15 year old child with a permit you should inform your insurance provider to see what their requirements are with regards to adding her to the policy.
As you are likely aware it is expensive to add a newly licensed child to an auto insurance policy since their risks to an insurer as an immature, inexperienced driver makes the insurance company charge more to cover them.
Since insurance premiums will increase when you put your teenager on your auto policy, you will want to seek ways to save money. Shopping around for the best auto insurance rates is important, but you can also looks for discounts.
Parents receive discounts for being married, maintaining good driving records, owning multiple cars and carrying homeowners insurance with the same company. For your child, your rates can be discounted if your teen gets good grades or establishes a good driving record (which takes time). Most companies offer discounts to students with good grades, generally a B average or higher.