The city has one supreme ruler: the Prince. But it also has a structure of government that is intentionally Byzantine. It was designed to keep any one group from amassing enough power to challenge the Prince, while giving everyone buy-in so that nobody important feels disenfranchised. And for 200 years, this has worked.
Prince Yaroslav is brutal and vicious and cunning and very intelligent. But he's also an amazing politician and military leader and the people like him because he has cultivated an image of heroism and magnanimity, and kept them safe from invasions. So his grip on power is solid - but like I said he's dying. And worse than that, he had murdered his way into power. All his mail relatives are dead and he's too old to have any kids. Since the city-state is run through male primogeniture, his line is about to go extinct, female descendants be darned. So there's going to be an enormous power vacuum here, both for his personal fortune and for control of the city.
His duties fall in three parts:
First, he is the head of state and the prime diplomat for the city.
Second, he is the first general of the army and the first admiral of the navy.
Third, he is a beacon for the people and keeps them loyal to the city first and foremost through clever popular initiatives like calling festival days and official ceremonies of honor, remembrance and celebration.
The second faction of main powers are four main guilds. Remember that this is a port city and the economy runs on trade. So every worker is in some guild and the guilds are the units of political power - rather than individuals, it's guilds and guild membership that grant people their voice. (This is essentially anarcho-syndicalism, but we're not going into the political science of it.) So the four guilds that have the most power are:
Weights and Measures (they handle currency and bullion as well as enforce trade standards),
the Dock Workers (strength in great numbers),
the University (they have spies and a magic college) and
the Merchants Guild (the owners of the ships and caravans.)
These four guilds wield the greatest power at street level.
There are a total of 96 guilds (the number varies a little over time) and and they come together in a deliberative body called The Peerage. The big four guilds send many voting members to the Peerage; some guilds like the Farmers or Wax Chandlers send only a few. The Insurers only send one!
The Peerage deals with day to day management of the city and also elects the Mayor who is responsible for executing the laws of the Peerage and the decrees of the Prince.
A third faction of main powers in the city are three minor noble houses. I haven't named them or any of their people or determined their strengths and weaknesses, but the main thing is that they're Old Money and backward-looking. They represent tradition and traditional values and the old ways that had worked for so long.
The three noble houses appoint people to a second deliberative body called the Senate. They have oversight on laws but no direct power to pass their own laws. They do however have the power of the noble houses and the money they can bring to the table, so they can put personal and extra-institutional power on the Peerage as a whole and on individual members to make corrections to Peerage legislation that they want.
There are two churches which are sanctioned within the city. I have not named them, but one is Lawful and the other is Neutral (and welcomes Chaotics.) I think these will be named after Dave and Gary somehow because I like that idea. I also think that they will seem somewhat alike to most people and the religions get along in public. Like Catholic and Protestant or maybe like Catholic and Jewish.
There is a third religion, the old religion of the Druids, but all Druids have been outlaws for 200 years.
These two sanctioned religions have no deliberative bodies, but since the leaders of the guilds are also involved in church leadership, their will is seen to as a matter of course and the churches' values are woven into the society.
The Prince, for his part, leaves the city management to these various groups - although he and his advisors keep a close watch over all of it and push and prod things to their liking. The Prince may personally call upon any of these leaders and make his desires known, and for the most part his will is done.
But now the Prince lays dying, and the whole system is ready to spring apart like a watch wound too tightly. House Triskelion, the house of the Prince, is about to go extinct. Therefore the three minor houses see this as their chance to advance themselves to primacy, just like the four main guilds do.
While the government is nominally working away and the Mayor is actually keeping things running day to day, the three noble houses and the four main guilds are consolidating their physical territory and martial power and literally shifting to a war footing. There will be diplomacy and war within the city. Ruined areas will be recaptured and put to use and there may indeed be blood running in the canals before long. Everyone is just a little bit on edge.