What follows is purely conjecture, and represents nothing but my vision of the Gorn and their government.
Since the Gorn opened their borders to diplomats in 2301, Federation researchers have studied Alliance history, culture and politics to better understand the motivations of their enigmatic neighbors.
The Gorn developed on a tropical world with several large predators, where competition for prey was fierce. They learned to be crafty and methodical to survive, studying their competitors' habits as well as the habits of their prey.
This competitive nature passed on through generations, creating a strong culture that placed the clan above everything. Instead of forming governments under chieftains and monarchs, individual clans in a region allied with each other for mutual defense and trade. Clan guzzaren (archons) consulted each other on policy that affected the alliance, but remained mostly independent otherwise. It was this early cooperation that would eventually form the basis of a world government in 2179.
The Gorn Alliance, 2179-2340
The Gorn had been a warp-capable species for nearly 15 years when they made their initial First Contact in 2177. Members of the Ugarza clan landed on an industrial pre-warp planet to make exclusive trade agreements with the planet's leaders. The opportunistic locals instead slaughtered the Gorn visitors, taking their ships in the process.
When the news of this reached Gorn itself (because the ship was later captured by Bazzan'r clan warships and the prisoners interrogated), many clan leaders were infuriated by Ugarza's subterfuge (the resulting loss of a ship being secondary). Clan leaders assembled, and within a year had hammered out the Planetary Treaty of Alliance. All but six of the 73 major clans signed the treaty in 2179, the holdouts eventually realizing they were better off allied than not by 2181.
The Gorn combined their individual clan forces into the Alliance Navy, controlled by a Central HQ that was appointed by the clan representatives. The only real centralized authority in the Alliance, Central HQ quickly gained influence and expanded, developing Exploration, Diplomatic and Shipyard arms; highly organized fleet command; fleet and skirmish-level ship-to-ship tactics and extensive planetary assault strategies; and standardized training. By 2215, Gorn service members thought of the Navy itself as their clan, giving Central HQ enough prestige to earn a seat on the Council of Guzzaren.
Central HQ further reorganized the fleet by awarding standardized construction contracts to the various clan designers, and reorganizing the designers into "bureaus."
The Navy began to meticulously visit and catalogue every planet and colony in the "Gorn Sphere of Influence" in 2236, looking for potential terraforming candidates and future client states. When they came upon outposts of a previously unknown race, Central HQ decided to test the strength of this new entity.
The Blue Flags
The response to their "test" was surprising, as the Gorn weren't prepared for an entity that was as powerful (if not more) as the Alliance. Instead of retaliating for the death of a decorated captain, Central HQ instead decided to sit back and study the new neighbor, only periodically poking and prodding the "Blue Flags'" outposts.
Their meticulous study of the Federation provided knowledge of other species, and the Gorn soon had their eyes on the Romulans and Tholians, as well.
Age of Diplomacy
In 2299, after 32 years of study, Central HQ decided that it was time to fully introduce the Federation to the Alliance. Sending four highly-respected diplomats under a white flag to Earth, the Gorn established relations with the Federation and agreed to a limited cultural exchange. Alliance-Federation relations were normalized in 2301, and both cultures began to study each other in detail.
Diplomatic overtures toward the Alliance's other neighbors proved less fruitful. The Tholians were too unpredictable and resisted any attempts at study, protecting their territory with a ferocity that startled even the Gorn. The Romulans were just plain unlikable, and the two governments quickly developed an animosity toward each other, resulting in minor skirmishes along the border.
As with the Federation, the Gorn have given other races nicknames: Tholians ("Bugs"), Romulans ("Birdies"). So far, the Gorn won't admit to a nickname for the Klingons. Some speculate that this is because they actually respect the Klingons as a species.
The Gorn Empire, 2340-present
The ascension of charismatic Grand Admiral G'ssenza to the position of Central Commander in 2336 began a series of events that eventually led to the Imperialization of the Alliance.
G'ssenza instituted many reforms within the Council, using his political influence to ensure he was able to get what legislature he needed passed. By 2339, when many Council members realized the Commander's final plan, G'ssenza had enough political support to raise himself above the Council itself and name himself Emperor of All Clans.
Resistance was initially fierce, but the threat of Navy involvment and the promise of political power to his opposition cemented his position by 2340, and the Empire was born.
However, besides name changes and the new central authority that superceded the Council and Central HQ, little changed. The government operated much as it had before, deferring to the Emperor's final decision on matters of state.
Government
The individual clans operate much as they have throughout the centuries. Each Gorn knows his place within the family, and each family knows its place within the clan, and the Guzzar speaks for the entire clan. How a Guzzar is selected is left up to the individual clan, and there are almost as many methods of selection as there are clans on the Gorn homeworld.
All judicial disputes (criminal and civil) are handled at the appropriate level within the clan. If a dispute involves two different clans, then an official from an unaffected clan is often appointed to arbitrate the matter. Disputes between guzzaren are handled by the Council itself. In the Imperial Era, the Council will often defer to the Emperor's decision.
The Council of Guzzaren is a body made up of the leaders of the 86 "major" clans and the Central Commander. They meet as often as "necessary" to pass legislation and decide upon policy. In pre-Imperial times, Central HQ is given great lattitude to interpret policy as it sees fit. Of course, the Emperor is the final authority in all affairs of state after 2340.
Modern Relations
The Gorn and the Federation-Klingon Alliance share a mutual respect, and the Empire has no intentions of disrupting the current arrangement. The joint colony on Cestus III is a testament to the growing friendship between the Federation and their enigmatic neighbors.
The Tholians continue to be unpredictable as ever, and they and the Gorn have fought occassional skirmishes over sometimes trivial matters. The Empire has decided to simply continue to study the Bugs and see what happens next.
The situation with the Romulans remains venomous, and the Gorn see the post-Dominion War era to be one of opportunity. While the Romulans were the least affected of the three major powers after the war, they were still weakened, and the Empire is starting to believe that some outlying systems may be available for the taking. Again, the Gorn are meticulously studying the matter, to determine if and when to strike.
The Future
The Empire has reached a state of stability after the bloodless coup 35 years earlier, and few, if any Gorn have actually been affected by the change in government. Emperor G'ssenza is still relatively young in 2375, and expects to sit another half-century on the throne. Nevertheless, the Council, the Emperor's family and Central HQ are debating how to handle succession, with no less than 15 proposals on the table. Despite the pressure, the Emperor says that he will make his final decision within 5-10 years.