Most likely by declaring a standard reference frame and encoding standards for indicating amount of drift from it, tolerance of drift, and standards for how to update against it. A particularly forward-looking standard would encode information about the standard frame used within it, so we could switch from Sol-standard to galactic standard to cluster standard.
Universal time is, of course, impossible in a relativistic universe, but (no sarcasm) that doesn't prevent us from trying, and getting to "close enough to work with for reasonable amounts of effort". Just as only a small portion of the world works on UTC directly right now, this time standard would be something computers would translate for people. Traveling at 80% the speed of light away from Earth in Earth's frame means you wouldn't want to directly use the resulting definition of a Standard Second for human time, but computers would be able to work with it.
An interesting challenge might be the computational cost of conversion to the "standard" reference given a speed near c. If a single CPU tick takes a "standard year" to compute how do you do you account for all ticks in your calculation?Is it possible to get to a sub-year standard time resolution in that scenario?
Universal time is, of course, impossible in a relativistic universe, but (no sarcasm) that doesn't prevent us from trying, and getting to "close enough to work with for reasonable amounts of effort". Just as only a small portion of the world works on UTC directly right now, this time standard would be something computers would translate for people. Traveling at 80% the speed of light away from Earth in Earth's frame means you wouldn't want to directly use the resulting definition of a Standard Second for human time, but computers would be able to work with it.