It's a big part of "the word for world is forest". A colony on one planet has essentially become self governing, until one day a ship delivers an instantaneous communication device, at which point the planet is back under imperial control. There's more to the story than that ofc
There's also "The Dispossessed", where an anarchist movement travels to a distant planet in order to set up their own government.
The Dispossessed describes an anarchist society on the impoverished moon of a verdant planet, and a scientist's struggle to reconcile his anarchism with his wish to further his research, which requires more resources than the anarchist society can provide. It is one of my favourite books.
I also don't remember distant communication being relevant for The Word for World is Forest. That's far more about the conflict between the natives and the colonizers, and passive vs. aggressive societies.
Distant communication is what establishes the setting in "Forest". At the very beginning, it is stated that the colony is 27 light years away - a frontier - and as the story progresses, there are hints that this is one of the reasons why the colonists can get away with brutalizing the local population, going far beyond the mandate that they have.
And then when they get the ansible midway through the story along with an inspection party that promptly reports their findings back to Earth, they start getting a steady stream of orders banning their various practices - slavery, violent reprisals etc. And when the local administration tries to implement some of those bans, the more hard-minded colonists deliberately provoke the natives into an open uprising by massacring their village. So it's a major plot driver, too.
There's also "The Dispossessed", where an anarchist movement travels to a distant planet in order to set up their own government.