More than any other aspect of the game, psionics is subject to Referee approval. Even if you're sticking with Chartered Space, unless you actually go into the Zhodani areas it need not play any part of your campaign. A Referee is within their rights to outright ban it for PCs, make it freely available to them, or change the rules about how psionics work.
It's in Traveller because it was a common thing in the pre-1970's science fiction that influenced it. Psionics is in Star Trek. Psionics (The Force) is in Star Wars. It's space magic and varies from work to work as much as fantasy magic does, but unlike the constants of physics or people.
However, you have a practical issue, having indeed rolled up a Psion and were looking for practical advice, not generalities.
My advice is to treat it less as a weapon with a magazine and ranges and durations, and come from a more organic approach. An unopposed Psion basically makes their roll and gets what they want, getting more if they roll better. In that way, it's like most skills.
And like most skills, you often don't need to roll. Roleplay it up and see how it flows. Just being a Telepath or Clairvoyant gives the Referee the excuse to feed you hooks and other information, same as they might feed drunken rumours to a character who has high level Carousing regardless if whether they were seeking that out. Concentrate on character over mechanics. He's a burned out Scout with a murky past. She's a standoffish Aslan who seems to be a better pilot and gunner than anyone would expect. You're a Psion, but what else?
I would also add that trust and integrity (or lack therof) is very important. What standards does this character hold to? Who knows about their abilities? Is there a campaign code of conduct for trained Psions? Are they monitored? Subject to licensing and review? Feared? Hated? Hunted?
Trusted and honoured?
Worshipped?