10 U.S.C. § 508

(a) No person whose service during his last term of enlistment was not honest and faithful may be reenlisted in an armed force. However, the Secretary concerned may authorize the reenlistment in the armed force under his jurisdiction of such a person if his conduct after that service has been good. (b) A person discharged from a Regular component may be reenlisted in the Regular Army, Regular Navy, Regular Air Force, Regular Marine Corps, Space Force, or Regular Coast Guard, as the case may be, under such regulations as the Secretary concerned may prescribe. (c) This section does not deprive a person of any right to be reenlisted in the Regular Army, Regular Navy, Regular Air Force, Regular Marine Corps, Space Force, or Regular Coast Guard under any other provision of law.