Political story arcs require the passage of time to come to fruition. It takes time to build up an issue. It takes time to develop a plan. It takes times to execute that plan. It takes time to see what happens after the plan has been executed. This is how real governments work and have always worked; for whatever political story arc you want to introduce you need time to pass within the campaign to play things out properly.

This can be challenging for GMs when they're running a campaign where things move very quickly within the setting. For example, consider D&D where you can have PCs advance very quickly over a relatively short period of time. It can be hard in these situations to develop an effective political story arc, really simple ones are doable but more detailed ones are difficult at this pace. A lot of RPGs that incorporate political elements often are designed to speed up the passage of time within the setting; an adventure might represent an entire season of the year.

Why is this necessary?

Consider you want to explore a story arc when the PCs are exposed to the corruption or incompetence of the government that rules their homeland. It could take a few adventures to subtly develop this narrative; you could hammer the message home in one adventure, but building things up creates a better narrative. It gives the players time to figure out how their PCs will react to the situation. As a GM you don't want to force your PCs down a path; if you want the PCs to topple the government then you are going to force them down that path. Why? The better story is always where the players want to go. Maybe they want to ignore the situation or move to another land, these options may not sound as heroic but this is where they want to go. Being patient as a GM is critical to be effective. If you give them the opportunity your players will find a great story and it might surprise you. Often players want to take the scenic route to resolving a big story arc.

How can we slow things down?

The first thing to remember is that players run their PCs as bigger than life characters in one important way - PCs aren't procrastinators like we all are in real life. Often if PCs see a problem they want to tackle it immediately. If they have an enemy they want that enemy eliminated now! This is great and what you want but this can create a tense dynamic between the passage of time you want to create and the workaholic take-charge personality of PCs. The best approach is to work this into the narrative.

"Okay guys you have a great plan for remodeling your new space station - next session we'll jump four months forward after the renovations are done." This is simple and you're rewarding the PCs by allowing their plans to move forward without you running a few adventures where you create challenges for this process to keep it 'dramatic'. You can stretch out travel time, force the PCs to winter due to the deep snows or ion storm activity, and just say sometimes, "okay you spend a few weeks in town making friends and spending coin, but now you're on the road again."

Players are happy to accept this as long as it doesn't disadvantage them, I mean if they have a nemesis plotting their immediate destruction and you tell them they just spent two weeks socializing then they will rightly be upset. To counter this you need to say that everything is going to be okay. "The Duke has a lot of other irons in the fire at the moment and you all are probably on the bottom of his list."

The passage of time is essential for the setting to organically develop. From my experience GMs are pretty good at evolving their setting rationally, but a little chaos is necessary. One thing I have done over the years is to randomly roll to see how an event, like a battle, war, or election, plays out. Another option is to empower the players to make some calls on aspects of the setting. Sometimes I have other GMs decide an outcome or two. The results in all these situations are different than what you might have done, but that's the point. These alternative inputs will make your setting more dynamic and real. On the other side is the fact that societies are fairly static, yes, they change but not quickly and certainly not without resistance - this is true even when change is for the worse.

Okay that's enough time on this subject...