Thanks for your question, John.
Once any dual citizenship issue (as covered by Section 44(i) of the Australian Constitution) is resolved, the Governor-General can reinstate a former Minister to the position he or she previously held.
The appointment of Ministers of State is dealt with in Section 64 of the Constitution which states that “The Governor-General may appoint officers to administer such departments of State of the Commonwealth as the Governor-General in Council may establish” and that “Such officers shall hold office during the pleasure of the Governor-General”. The 'Governor-General in Council' refers to the Governor-General acting on the advice of the Australian Government.
The only restriction is that “...no Minister of State shall hold office for a longer period than three months unless he is or becomes a senator or a member of the House of Representatives.”