Even though you have been ticketed for driving with a suspended license, there are insurance companies that will insure you; however you will need to be able to reinstate your driver's license within 30 days of the inception of your policy.
If you are not able to get your driver's license reinstated within the 30 days then it will be difficult to get insurance on your vehicle since an insurer wants a valid license to rate you on. While others could get insurance on your vehicle, even they do not have insurable interest in your vehicle, to drive you around during your suspension period with companies such as Esurance that allow this it still may cause an issue with your lien holder.
Normally when you have a loan out on your car the lien holder requires you to have the insurance in your name. Without having insurance on the vehicle your lien holder may be able to repossess it or they may instead put forced placed insurance on the vehicle. This is expensive insurance that protects the lien holder's asset but does not include Liability so would not be even the minimum insurance to keep your registration good in most states. This forced insurance cost would usually be added to your car payment.
You can speak to your lien holder to see if they would accept insurance in someone else's name or if there is any method that would satisfy them to have insurance on the car while your license is suspended and you are unable to get insurance on the car.
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