I envy you your innocence

Take it, your imagination, and run with it. Run far! Don't mind the history
Our group's best times (rose coloured glasses maybe) playing Traveller were before we knew much of anything about the OTU (aka Original/Official* Traveller Universe). We rolled our own worlds and subsectors and just went out there into the unkown to trade, hire our guns, run down rumours of glory, etc. etc.. Pirates, greedy merchants, crazed religious zealots with heavy ordnance repeatedly blowing up the Starport around us, a Scout with an apparent death wish engaging the jump drive at 10.1 diameters (or less) for the rush with the excuse they were collecting data on misjumps to break the J6 limit...
...of course all this was in the heady days of just a few simple LBBs (little black books) in the late 70's...
Sorry, rambling
More on topic. The Imperium banned Psionics several hundred years ago. After a long period of free practice and investigation of it. Reasons are unclear. Since then Psionics are frowned on at the least. CT (Classic Traveller, the first rules) had a table of reactions if one was found or suspected to be Psionic, covering such reasonable responses as: tarring and feathering, forced lobotomy, or lynching. Truly it was an enlightened age.
Since then Psionics in the Imperium has operated underground, in fear, though some suspect The Imperium unofficially operates secret Psionic agents this is officially denied and there are no witnesses or proof. Things are different outside the Imperium. The Zhodani (sworn enemies of the Imperium) have embraced Psionics. IMTU the Solomani (we, first Humans, of Earth and the Confederation) use it as a tool with regular testing and indoctrination of the talented into an elite agency.
This Psi Corps you speak of doesn't ring any bells (unless as suggested it is B5 related, they did have a Psi-Corp) but then I don't have the Psi book (or B5) and haven't really digested the Core book yet. Sounds like a MGT variation offhand.
* whatever the difference means in MGT lingo, I can't keep it straight, basically what applies to the Imperium does not necessarily apply to MGT and/or vice-versa, or something like that.