The political dynamic of a kingdom can be used to create new challenges for the players as they enter regions or need to address the leaders. While it isn't always the simplest method, there are political formats that could cause players to have to think differently in order to address the leader. One option is to take existing government styles and apply them to a town/city since not every city in a civilization will conform to democracy or royal lineage. Options include:
Aristocracy
Rule by elite citizens. An aristocracy is a government by the "best" people. Aristocracy is different from nobility, in that nobility means that one bloodline would rule; an aristocracy would mean that a few or many bloodlines would rule, or that rulers be chosen in a different manner.Aristocratic governments would be similar to a combination of a council ruling with a touch of royal lineage where the "best" pass down their rule. Players encountering this government may have to address multiple members to sway their favor to earn a majority opinion in their needs.
Kratocracy
Rule by the strong; a system of governance where those who are strong enough seize power through physical force, social maneuvering or political cunning.Kratocratic governments would be a good system of government for more brutal organizations like raiders, orcs, goblins, etc. Players encountering this government would need to complete to show their dominance and power to be deemed of worth.
Kleptocracy
Rule by thieves; a system of governance where its officials and the ruling class in general pursue personal wealth and political power at the expense of the wider population.Kleptocratic governments would be ones where bribery and favors would earn the players merit, but as the government is corrupt, it is just as easy for a better offer to arise creating potential for enemies to be made.
Anocracy
A regime type where power is not vested in public institutions (as in a normal democracy) but spread amongst elite groups who are constantly competing with each other for power.Anocratic governments would be in constant change and would essentially be warlords competing for power. With constant power struggles, it may make it difficult for the party to gain favor without involving themselves in the power struggle.
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While these are only a few options that you can incorporate, you can still even mix-and-match these together. In my small campaign, the region that the players are in are ruled by monarchies and democracies, but they are overseen by a collective representative democratic organization that hold a higher power than the rest. This organization, called the Catharsis, are elected by local cities and meet as a region with their faces covered to protect their identity so only their region know who their Catharsis member is. This organization deals with peace in the region and essentially acts like the FBI and CIA or the region and oversee the power of the region. This layering of power puts a level of unknown into the players when they deal with any leader because they now have 2 organizations to worry about.
By adding a new form of government to a civilization, conflict can arise between areas that could result in wars, diplomatic encounters, or perhaps even adventuring to gain favor. It can add that little difference in the campaign that breaks up the monotony of the monarchic leadership, and leaves the door open to bring change and conflict to a region as a result.