This empire was founded on the basis of a triumvirate with each leader governing their own spear while being prevented from interfering with the others. The clerical spear is made up of the nation's official religion. It is led by priests and their functionaries, who control all matters of faith and how it is administered to the people. The political spear is controlled by the administration. This administrative body controls matters dealing with the economy, formation of laws, and everything necessary to keep society running. The military branch is controlled by its generals. This is the army that defend the nation from outside threats. Each of these branches are controlled by a king, who is the ultimate authority in each of their own spears. Together, these figures are known as the TRIPLE T (THE TRIUMVIRATE OF TERROR).
These three kings are equal in power to each other and have final say in matters due to their branch. They also serve as a balance between each other. Unfortunately, a problem arises with the military king. Generally the force with access to the most powerful weapons have the most influence, and there is little to stop them from taking over the government entirely, or forcing another branch to act in their favor.
As powerful as religion can be, faith loses to guns. Administrative power also lose to guns. I need a way to keep the military king in check to prevent him from overthrowing the empire, and design a system of checks and balances where each branch doesn't infringe on the other. How can I do this?