"The mutual recognition model of nurse licensure allows a nurse to have one license (in his or her state of residency) and to practice in other states (both physical and electronic), subject to each state's practice law and regulation. Under mutual recognition, a nurse may practice across state lines unless otherwise restricted. This is referred to as a multi-state nurse licensure model, specifically referred to as the Nurse Licensure Compact (NLC). All states who currently belong to the NLC, also operate the single state licensure model for those nurses who do reside legally in a NLC state or do not qualify for multi-state licensure."
In short, if your residence and state of licensure is in a compact state, you are free to work in other compact states without the necessity of applying for a new license. Your existing license is sufficient!