Insurance companies differ on their guidelines for non-owners insurance so some might have age restrictions while other companies will not. You need to comparison shop to find the company that is right for your needs.
If you are young and living at home with parents or relatives it is usually easier and cheaper to have you put onto their current insurance policy. If that is not feasible and if you do not own a car but are licensed and occasionally do drive, non owners is a type of policy that could work for you. It is important to ask when shopping for this insurance, if you will be covered for vehicles owned by members of the same household because some companies do not allow this.
Get started on non-owners auto insurance comparison shopping here.