In my last post I drew a parallel between telepathic animals and legends about magical animals. In an SF setting with psionic powers like telepathy and telekinesis there is the possibilities that legends of magic were accounts of primitive psionic use. Surely the view of Traveller where Psi is mistrusted and feared has parallels to the Witch Hunts of history.
The difference is that Psionic Institutes and trained Psionics are a lot better at defending themselves.
Psionic Institutes are very rare only being found on high population worlds (billions or tens of billions of people). I suggest the high population helps to hide psionic individuals from scanners that could pick them out of a crowd. This probably only applies to untrained individuals.
What happens to untrained individuals who are caught is up to the referee. Execution, lobotomy, enslavement, or chemical treatments to remove psionic strength are possible. If there are drugs that suppress psionics then they may be widespread and introduced into food or water supplies by particularly draconian authorities. Part of psionic training might include a proper diet to avoid these effects.
I leave imagining a farmers' market staked out by Men In Black to your imagination. An adventure can start anywhere.
Even if a branch is located ("There is no branch here. Go back to your friends. Enjoy your shoreleave. Spend your creds on ale and whores.") it may require some travel to get to. So your attempts to find a branch are just the first hurdle. For some travel that may include a trip to one of the other worlds of the system. After all remote locations are hard to come by on high population planets. Part of the location process may involve screening and manipulation by powerful psionics. If you can't resist the suggestion to go away you aren't a powerful enough talent to bother with.
Some Institutes may provide clues to people they deem worthy. Think suggestions to play a creepy game on the internet or a hunch to be at a certain place at a certain time. A generous referee could allow an untrained but high power psionic some involuntary use of their powers, vision, hunches and lucky breaks, necessary to follow the clues to the Psionic Institute. In fact the Institute might not even exist as a discrete place but take the form of a group of secret masters constantly moving around. In this case the Institute might find you.
A society that does not trust psionics might keep psis separated from the buzzheads on their own planets or space colonies. Misinformation programs might paint the reservation as a plague area or simply uninhabited and reserved for military or government use. In this case finding the Institute is a matter of finding the people who can smuggle you across the border/blockade (or provide the means for you to sneak in).
Finally a Psi Institute might consider doing an outreach program to less developed worlds, grabbing developing psis before the torch toting mobs. They might very well present themselves as magicians to less developed cultures to rely on shock and awe rather than violence to achieve a rescue. Some over the counter tricks and illusions could help. A stage magician with TK would be awesome indeed.