If you find your driver license has been suspended, you will need to get your license reinstated in the state where it is suspended,
before you can get a driver license in the new state. Click for more information.
It may be easier to get your license reinstated before moving, at least check with the state DMV where your license is suspended in before you move and see what needs to be done. State DMV information can be found here.
Once you have moved, your only option would be doing everything by mail and phone.
If your driver license is eligible to be reinstated, you may have to file an sr-22 certificate with your car insurance company.
Once you get your license reinstated, you can apply for a driver license in the new state.
To avoid having to get two auto insurance policies, it is easiest to find an auto insurance company who writes business in both states.
You will need auto insurance in the state you are driving, and you may need to keep the sr22 filing in the state where your license is suspended for a while.