It's not hard. An atomic clock or the 52nd century version of it is going to be standard equipment for Imperial locations, and while there are very, very, very small discrepancies, if you are just needing HH:MM:SS time your ship can synch its timeclock at any starport or orbital landing sat controller.
Your personal comps are going to be based on whatever time you want. Your ship may follow it's own cycle, and you'd have your planetary local time, or IST. Though unless you are doing something that requires IST, local time / ship time is going to be your guide for all your activities. Ship crew MIGHT run on a 24hr clock, they might not - depending on the ship and crew and what is the norm. Stations may have their own time periods and be different than the planet they orbit - if it makes enough sense. A planet with a 14hr day might now work for a station, nor would a planet with a 37hr day,
Unless it's key to an adventure, stay with a 24hr clock since it's far easier to keep track of in game.