No, normally if you lose your license in one state, due to suspension or revocation, than you cannot just move to another state and obtain a driver's license there. All states now communicate with each other especially regarding what they call problem drivers.
All states check the Problem Driver Pointer System (PDPS) and/or National Driver Register (NDR) to see if a driver's license applicant is listed.
The PDPS helps search the NDR which is a central database of information on problem drivers (those whose license has been revoked, suspended, canceled or denied or have been convicted of serious traffic related offenses) provided by all 51 US jurisdictions.
Based on information received as a result of an NDR search, PDPS will "point" the inquiring jurisdiction to the State of Record, where an individual's driver status and history information is stored. The PDPS is intended to assist jurisdictions in the meeting the basic tenet in the US that "each driver, nationwide, have only one driver license and one record."
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.
If you are moving and need to obtain a license in new state, you will typically need to clear up the issue in the state where your license has been suspended or revoked so that you can get it reinstated and your name off of the NDR so that you can apply for a license in a new state.
If you have an issue in one state with your license you should contact your Department of Motor Vehicles to see how to get your license reinstated so that if you are moving to a new state you can obtain a license there. If you are unable at this time to get your license back in one state than you can contact the DMV of the new state to see about applying for a driver's license there however it is doubtful you will be able to receive one until your out of state issues are cleared up.