Section 1, Subsection 2 of the Charter of the Lazarus Regional Guard reads
(2) The Delegate will be the commander-in-chief of the Regional Guard. The Prime Minister must appoint a Cabinet Minister to serve as operational commander of the Regional Guard, subordinate to the Delegate and subject to approval of the Delegate and all provisions for appointment and removal of a minister. Operational command authority may be further delegated to a chain of command subordinate to the Cabinet Minister.
Article IV, Section 7 of the Mandate:
(7) Cabinet Ministers will serve until the end of the Prime Minister's term or until resignation, removal from office by the Assembly or the Prime Minister, or automatic removal from office.
As such, all Ministers, including the Director of the Guard, are dismissed upon the Prime Ministership falling Vacant.