N.J. Stat. § 38A:3-5
The deputy adjutant general shall be appointed by the Governor upon the nomination of the Adjutant General. The deputy adjutant general shall be a person who has served as a commissioned officer in the armed forces of the State and who is a federally recognized commissioned officer in a military rank not below that of colonel. He may be appointed with the grade of brigadier general. The duties of the deputy adjutant general shall be prescribed by the Adjutant General.
The deputy adjutant general shall have the authority to act for and in place of the Adjutant General during the absence or disability of the Adjutant General. If the office of the Adjutant General shall become vacant, the deputy adjutant general shall exercise the powers and perform the duties of the Adjutant General until a successor shall have been appointed and shall have qualified.
Any vacancy occurring in the office of the deputy adjutant general shall be filled in the same manner as the original appointment.
N.J.S. § 38A:3-5