The Roman Empire was the government of the planet 892-IV. It was a parallel to Earth's Roman Empire. The Empire was divided into several provinces spread out across the planet's continents. (TOS: "Bread and Circuses")
The Empire was formed in the 3rd century by men who James T. Kirk described as parallels of Julius and Augustus Caesar. At the onset, there were slave rebellions, but they were always suppressed. As the centuries passed, slaves were given more rights (pensions, health care) and would no longer rebel.
The last major war on 892-IV occurred in Earth's 19th century. According to a Roman politician, after this time the Roman Empire had fought no further conflicts on their planet. It is unknown however if the Empire controlled their entire planet, since the Empire still held a concept of barbarians which indicated persons or civilizations from outside the Empire.
In 2261, the SS Beagle suffered meteor damage and sent down a landing party to search for iridium on the planet. The resulting near-contamination of the culture forced the government to respond. Proconsul Claudius Marcus appointed Captain R.M. Merik of the Beagle to the position of First Citizen of the Empire and required the Beagle crew to permanently live on the planet, all the while remaining quiet about their extraterrestrial origins. Those who refused, such as William B. Harrison, were declared barbarians and forced to fight to the death in gladiatorial games.
In 2268, the USS Enterprise also sent a landing party to the planet, while investigating the whereabouts of the Beagle crew. The landing party originally stayed with a group of Son worshipers, before being caught trying to enter the Empire's capital. The landing party was forced into gladiatorial combat before beaming away. Merik was killed helping them get away. (TOS: "Bread and Circuses")
The Roman Empire was a despotic state under the apparent absolute rule of a Roman Emperor. The Empire was divided into provinces each with their own local government and customs. Some provinces had little interaction with each other, as evidenced by Starfleet personnel, wearing Starfleet uniforms, easily able to pass themselves off as coming from "another province".
A Senate functioned as a type of legislative body while political leaders known as Proconsuls exercised near total rule over various areas of the planet. In at least one case, the Proconsul was responsible for overseeing gladiatorial games. The Proconsul was assisted in his duties by a First Citizen, who was sometimes allocated the additional title "Lord of the Games".
The Empire maintained various independent armies and military forces. Such forces, if necessary, could be joined together to form a "combined army" to combat a threat. The technology level of the Roman Empire was unknown, but it was once stated that one hundred men with hand phasers could easily defeat the combined armies of the entire Roman Empire. The Empire also had no significant form of space based planetary defense, as it was further stated that a single Constitution-class starship could destroy the entire planet.
In addition to military forces, the Empire also maintained a dedicated police force, one of whom's duties was the capture of runaway slaves.
In the novel The Captains' Honor, set 100 years after "Bread and Circuses", it is explained that the planet's alternate Roman Empire conquered their world by extending into all of Africa (or the equivalent of such) and using the captured resources and manpower to launch wars and take over the rest of the planet. This in contrast to the Roman Empire on Earth, which only held colonies in North Africa which were abandoned in the 4th and 5th century as the Empire began to collapse.