No, normally you cannot move to another state and obtain a driver's license (DL) there while your license is still suspended in your previous state.
All states check the National Drivers Register (NDR) when a person applies for a driver's license. The National Highway Transportation Safety Administration (NHTSA) is the administrator of the NDR and states that the NDR contains a listing of names and related identification, provided by State driver licensing officials, of those "problem drivers" whose driver's licenses have been cancelled, denied, revoked, or suspended or who have been convicted of certain serious traffic violations.
There is a federal requirement for state licensing agencies in the US to check applicants for driver's license against the NDR. This mandate is intended to help prevent problem drivers from "license shopping," meaning a person would go to a different state to get a new driver's license when their current license is suspended or revoked according to the NHTSA. Keeping problem drivers off the road is critical to the NHTSA's goal of reducing highway fatalities and injuries.
With a license suspension in one state you should be listed on this national database. To check and see if you are listed on it there is a form you must complete and have your signature notarized, and then mail the completed form to the National Driver Register. Forms that are not notarized will not be processed by them.You then can find out if you are listed on the NDR.
Typically if you have a suspended license in one state you must deal with the issues surrounding your driver's license there and get that license reinstated before you apply and obtain a new driver's license in another state. States will allow you to exchange an out of state license for a new license when you move to a state within the US, however the driver's license you are turning in needs to be valid.
If you are moving to a new state and your current DL is suspended you can contact the Department of Motor Vehicles for your new state to see what advice they can give you about getting a driver's license.