Switch your TV on.
Watch police-, FBI-TV shows. Also CIS, Columbo.
Mainly you are playing policemen, adapt those story to a future setting.
A murder has to be solved, drugs deals to be ended ...
So instead of car chasing there are space ships, didn't sound very interesting, but that would be a setting problem.
In the end there will be routine.
What you try, are city adventures (less action and more role playing).
It is a hard task (if I would try it with my group they would maroon me - actually they did).
OK, how to solve the problems:
Split the different parts of police investigation on different planets: The rich, the poor, the industry, the criminals, the agra-world.
(Of course the distinction is smooth: the successful criminal is rich, some poor try to get more by illegal means, the industrial workers want to relax with drugs, ...).
Now we have pretty much travel between the planets: Food, goods, illegal passengers, smuggling (drugs, weapons, persons) and therefore the necessity to control it.
To make the often traveling between the system exciting is a hard task.
There will be engines failure, EVA* repairs, there will be attacks (but seldom) to stop the investigation; "What is this signal about ? Seems to be a emergency beacon. Oh it stopped, we have to investigate now, no one else could find it again.".
You can even introduce some X-Files: Alien or normal human activity, what about the rumors of people who could read and even alter ones mind ? (Or if Psy is known, rumors about technology to power Psy up or give it to anyone.)
What is the political system the planets have ?
There are always seperatist (all planets), perhaps someone try to make a coup d'etat (a party or the military). What about religions - are there some fighting each other ?
Following the above there might be a plan to murder someone and the PC could be assigned as bodyguards. (but this isn't their normal business - but perhaps it belongs to the drug case).
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Sorry, for the mess above, but it was the result of brainstorming
Once again, investigation kind of adventures are hard to perform, good luck.
Switch your TV off, start adventuring.
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*This is an explation for me, because everyone here knows what EVA means:
EVA = Extra Vehicular Activity (out of the star ship in a vac suit).