I've been playing a lot of Battle Brothers lately, and the game has an "ambition" mechanic that I really like and that would fit very well for Starsector. It really works wonders to make the (open-world) game flow smoothly.
It would work like this: From time to time you can choose what your captain's next ambition should be. You can choose from a handful of semi-randomly selected options, or you can ignore the system and chose non at all. If you fulfill an ambition you get a small to medium bonus, if you cancel the ambition you get a small penalty. The clue is that every ambition is something that helps you understand the game's mechanics or explore the game's options and locations. These ambitions are supposed to:
1)Be a continuous (non-handholding) tutorial
2)Encourage you to experience parts of the game that you might otherwise not
3)Keep you from ever feeling lost and without goal, which can easily happen in a game that offers as much freedom as Starsector.
I wrote ambitions are only semi-random because some progression and pre-selection should be involved, depending on your level and what you already archived. Your ambitions grow with you.
It could start with something like "gain a contact", "buy your first combat-destroyer", "recruit an officer", "discover lost ruins" and "raid a market", and escalate to stuff like "get your first capital ship", "exploit a shortage", "intercept a trading fleet", "defeat a remnant station" or "discover one of the lost wonders of the Domain".
Rewards could be simply bonus XP, a small reputation gain with all factions or the occasional rare weapon or hull.