In the MegaTraveller universe of the Shattered Imperium and the Spinward Marches, the Psionics Institute was an underground organization that was a bit of an outlaw because of history. They had originally been sanctioned by the Imperium but once it was discovered they were connected with the Vilani Empire, the Psionic Suppressions followed which forced them to go underground. It became one of those secret things a character would be come part of that made them interesting.
In my universe, I wanted Psionics but I wanted them underground for a different reason. In my case it is simply the standpoint that humans still are prejudiced against the unknown. Humans are pretty proud of their technological prowess but when they face unknown forces or ideas no matter how advanced a society may get they react in fear which leads to hatred. In my universe, Psionics are either explained away or they suffer persecution. Mostly the Institute is rumored to exist but most consider it a legend and the Institute works hard to keep it that way as they feel normal society is not ready for who they are.
Psionic Powers in MegaTraveller were quite different but followed familiar science fiction patterns. There are not many changes at this point just that one of the things in MegaTraveller is the category of powers is Special. That could lead a lot of directions but usually the Game Master and the player would have to figure something out that was interesting and I have come up with a lot of different things.
The main issue of this saga of Ayn Jones, is that she will be on her own a lot and will often not have the skills or abilities she will need to overcome all the obstacles ahead of her. Unless she also gains psionic powers. That also becomes problematic. I don’t want her overpowered so I am trying to balance this talent with what particular psionic abilities she will have so that they don’t give her such a big advantage that she can do anything. My choices will be based on what will make her an interesting character with an edge but not make her a goddess in power.
Blessings and Cheers!!!