If a last will was validly made while you were living in another state, it is probably valid in your new state. However, if your last will was not "self-proved," it may not be accepted by certain courts until a witness signs an oath swearing that he or she saw you sign your last will. Because of the expense involved in finding your witnesses, it is probably best to rewrite your last will after moving to another state.
Most states allow a last will to be self-proved. The LegalZoom Last Will and Testament includes a self-proving affidavit in states where that is permitted. This means that if you move to another state, it would be unnecessary to locate witnesses before beginning the probate process.