I’m taking inspiration from Robert A. Freitas Jr.’s theory about alien metabolisms based on gravity rather than electromagnetism. He imagines astronomically sized beings that derive energy by arranging collisions between celestial objects or carefully regulating the contraction of objects. How ”fast” would it take for an organism the size of a small star cluster to think a thought (if they can think at all)?
Frame Challenge: It is a community, not a single organism
size of a small star cluster
If it needs gravity, and therefore mass to live, then it's body should be min-maxed to contain as much mass using as little resources as possible. Basically, star cluster sized gravity lifeforms would never evolve because smaller gravity life forms would outcompete them.
The ideal size for such an organism is planetary. It could grow to fill all the lakes and oceans sucking power from the tidal forces of the moon(s). Then to reproduce it would need to shoot seeds off into deep space that could colonize other planets with moons (or moons with planets might work too if they are not tidally locked).
Each tidal organism would be a separate entity, it probably would not need to think since it would have more in common with a tree than an animal, but if it could think, it's brain would likely be centralized meaning that it would have a small cluster of neurons close together in one spot so that they can think quickly. Thoughts would happen just as fast as ours, but responses may take much longer. If their nervous system works like ours, then chemoelectrical signals will travel through its body at up to 65m/s. On an Earth like world, that means that it could take up to 4 days for a signal to get from the brain to the farthest parts of the body... but it is unlikely that they would work like ours.
For starters, the speed of a chemoelectrical signal is largely limited by the length of a neuron. The time consuming part is the neurotransmission between cells. Within a cell the signal is electrical; so, if it has one really long nerve cell connecting the brain to the other side of the world, the signal could get there much faster depending on what kind of medium it is moving through. Or... it could use actual wires or fiberoptics to get going even faster than that and get the signal there in under a second.
Why they think, and how fast it would be
That said, communication between gravity organism may be important for mutual survival. A gravity plant on Mars might need more water; so, it asks Earth to send it some water, and in exchange it hits Luna in the backside with a Chicxulub sized asteroid to keep the moon from slowly drifting away from the Earth... and if the Earth refuses, Mars might decide to mug Earth of some of its precious water by threatening to toss a Chicxulub sized rock directly at the Earth.
Inside of a local planetary system like this most communication will take somewhere between a few minutes and a few hours if they can communicate with any sort of EM signals. Even if they can't broadcast radio waves per say, they could possibly use color signaling like cuttlefish to communicate between worlds at the speed of light.
All this said, communication between separate star systems will likely not happen since the delay would be over several light years, and actually sending/receiving signals over those distances gets very very tricky. The closest to "small star cluster" scale you will likely get is things like binary/trinary star systems, but they may still choose to send seeds off into deep space to colonize these far away places once thier home solar system is all filled up.
Probably slow, if at all
What is the background story around such an organism? How did it evolve? The race for intelligence has been mostly propelled by the predator-prey cycle. And second to that a complex search for food, when an algorithm of randomly stumbling around didn't suffice.
Since the organism lives on a different time scale it would have no need for a fast thought process. If might have the same type of intelligence as the "Slime molds" or protist. (Google: Physarum polycephalum)
The only thing it needs intelligence for is to detect and select celestial objects that are edible. And then it needs to plan a jump or split parts of and send them there to digest that body or system of bodies.
At a lower level it needs to coordinate orbital trajectories, but that might be partially subconscious. We are not aware of our blood sugar levels etc. But we are aware of the texture of what we eat and chew our food consciously until we feel we can swallow it. I imagine it feels like eating chicken wings.
But how did it came to be? One solution might be that it started as a swarm of space drones that were operated by an ancient civilization to tera-form planets. The drones are massive in size run on solar panels and can self replicate. Individually they have a sub human level of intelligence to perform basic tasks like asteroid mining and nudging object around to drop water ice rich objects on dry planets.
They behave quite predictably and are a very safe and lazy way to do tera-forming. You send a few of them to a star system and a couple centuries later the planets are tera-formed and ready to be colonized. Because of their limited intelligence they don't form a military threat.
That civilization destroyed itself in a war or ceased to exist for some other reason and left several swarms of the drones behind on an unfinished mission. These swarms were tera-forming bodies around brown dwarfs and other smaller star like objects. Most of them died out eventually or got in contact with other civilizations in denser parts of the galaxy. Who perceived them as a minor pest and cleaned them up.
A few were lucky and got to spread around in a largely ignored part of the galaxy and started to tera-form the smallest of brown dwarfs and even the larger rogue gas giants. Those don't emit much light, and certainly not in the spectrum usable for their solar panels. Unless you drop something on them. Or even better when they find a twin body and let it collapse.
With these conditions they evolve better swarm algorithms and become better and better at increasing the output of small stars and even igniting large planets. Even if the planets don't start fusion, the heat that is generated by the material that falls in the deep gravity well of a gas giant can make it shine for millennia. Enough for the drones to start the self replication process.
And so an artificial live form was born.