I'm working on a story that involves intrigue, so got some tips:
1-Intrigue plots are as plot driven as much as they are character driven: A solid general rule to follow is that characters make the plot happen. For intrigue to work, you need a proactive and driven cast with their own motivations and willing to act towards it.
2-Intrigue requires conflict: this may sound obvious, but to get people to oppose each other, you need characters with goals that are incompatible to the goals of other characters.
3-Alliances can keep things fresh: Not all goals need to be incompatible. this can lead to the creation and development of alliances. Some may be genuine, but others could be a betrayal expecting to happen.
4-Introduce your cast and plot points gradually: be it an intrigue plot with a large cast and many factions plotting against each other, or two cunning folks in a secret power struggle, you don't want to overwhelm your readers with information.
5-Play with different levels and kinds of intelligence: Some people are book smart, others are street smart, others come at different mixes of both, and others just don't have what it takes in the game of intrigue (but may be strong in other aspects).
6- Foreshadowing and twists: As a general rule any plot twist needs to make sense in hindsight, so make sure you have a clear idea of the character's motivations and plans before they happen. Also, dropping hints of events or plans to happen can be key to keep readers engaged and making theories.
7-Reveal half of the hand, but hide the aces: this is connected to the previous point. You don't need to reveal all the plans, but you need to give enough information for the readers to follow what's going on, but hide enough to surprise them. This is a tricky balance to pull of, but the pay-off will be worth it.
hope this helps!