In most cases, this is not a factor until you purchase a new policy or renew an existing one. It is not considered a moving violation unless you actually received a violation for "driving with a suspended license". Some insurance companies may penalize you by taking away a safe driver or renewal discount. In most cases, you will be required to get your license reinstated and show some evidence of this.
You can find out here what your rate will be with a suspended driver's license.