An important character who emerges throughout Ramayana is the Rajguru, probably the Prime Minister as well, Sage Vasishta. He remains composed, speaks with measure and attends to all affairs of the state and administration.

Even during Dasharath's death, you can notice him slip just for a moment as he laments the kings death, but he composes himself immediately, and starts to issue instructions as to what is to be done next. Takes the control of the state during the interregnum.

The same with the Kulguru of Ravana, Sukracharya who keeps dissuading him from his misadventures but still stands by the arrogant emperor till the end. He is the person who identifies the child discovered in the pool of Lanka to be Mahalakshmi.

And goes ahead to predict the downfall of the Lanka. He insists, against Brahman dharma for the child to be killed because he believes that it is the best for the Empire. (Finally agrees for it to be immersed in the sea)

The Kulguru of the Kuru dynasty, Drona serves as both the Prime Minister, and later the Commander of the Kaurava armies during the Kurukshetra War. He is invincible in the battlefield as long he wields the bow (We all know how he dies)

Vidura, the Prime Minister of the Kuru Empire is often the only sane voice in the chaotic stratagems of Duryodhana and the helplessness of Dhritarashtra. His loyalty to the health of the empire is demonstrated when he argues that a blind man cannot be king.

But he continues to serve as the Prime Minister when Dhritarashtra ascends to the throne. He is noted to be the sole protestor (other than Vikarna), to the humiliation of Draupadi in the royal court, aware of the destruction it forebodes for the Kuru dynasty.

He forcefully argues for a truce when Krishna comes as a messenger for the Pandavas, but finally resigns when Dhritarashtra refuses the terms and Kurukshetra becomes inevitable.

An example more historical would be Chanakya, who is both the Rajguru and the Prime Minister of Chandragupta who literally runs the empire, codifying the laws, and controlling the administration, establishing diplomatic alliances for the Nanda Empire.

And opposing him would be the Amatya Rakshasa, the Minister of the Nandas whose loyalty to them, keeps him sparring with Chanakya to save the tottering Nanda rule. (Finally becomes Chandragupta's Minister as well)

Im sure you know that Sukracharya, as the Rajguru of King Bali, attempts to dissuade him from agreeing to Vamana's request for three feet of land, and ends up losing his eye in the process. The Prime Ministers keep putting themselves in the way of harm to defend their emperors.