You mean that from a remote place or fast-moving ship, the time on Earth would appear to go at a different speed? So local time would not just have a constant offset?
In addition, you will probably want clocks that run at a given perceived speed, to time physical processes that take the same time everywhere (e.g. so your cookie recipe saying "bake for 600 seconds" work without translation).
You don't need science fiction for this.
* https://www.bipm.org/en/bipm-services/timescales/time-ftp/Ci...