[Arkinsaw]

I always wondered how the Enterprise communicated instantly with Starfleet when they were light years away. Now I know!

Sometimes they could contact them immediately, and sometimes Kirk had to make his own decisions because they had no immediate contact.

[Lunatic Fringe]

Yes- actually several ST episodes had to deal with the fact that communications still took some time to reach Earth. The "instant messages" we see in some episodes usually took place when Enterprise was relatively close to Earth.