As I understand it, we originally kept track of time basically by the sun.
From these observations we settled on 86,400 seconds being the length of day, and then we changed our definition of day from "one rotation of the Earth" to "86,400 second" as measured by an atomic clock.
Now, we spend our time adjusting our "real" time, the one we humans use, to sync up with the atomic clock. This is where leap seconds come from.
We measure the earths rotation by measuring when the meridian passes certain celestial objects (like the sun, but also other stars and quasars). Apparently we can achieve and accuracy down to 4ms.
So, our concept of time is bound to an atomic clock(s) somewhere, and pretty much everything else is synced to that.
Now, you can not fly atomic clocks around. If you do, they get out of sync. Relativity, et al.
Internal to the solar system, I think a radio beacon would be suitable for keeping system time in sync. "At the sound of the tone, it will be 1:00:00 AM…*ping*", in this case the receiver will "know" how far they are from the transmitter, and be able to compute the lag with reasonable accuracy.
So, if a ship flies to 100D, and does a final sync, and then Jumps, we know, when they entered jump space, their internal clock matched the standard clock.
What we don't know, is whether jump space skews the clock at all or not.
If not, then when the ship arrives, a process of establishing location, velocity, etc. can take place, and a new ping can be sent to the system standard clock and ideally the system clock is now synced to the standard clock.
However if jump DOES skew the clock, how deterministic is it? If it's deterministic, ideally it can be compensated for, and syncing happens.
If not then…moving clocks around won't sync up the empire, something else will have to do. Not quite sure what, however.