I'm not Finchy, but you get Psionic abilities/ a way to spend Exp as a Delve reward for beating the boss of Synthech Admin & Research. (The Building at the North-East of Westview.)
Oh, I see, sorry!
You can acquire Psionic skills by using the chair in the east wing of your Safe House. There are many other upgrades there as well, that you can acquire by exchanging EXP.
The southern purple section of the upgrade area pertains to Psionic abilities, so you can find several there. Hope this helps!
No... Okay, I'll word it our more clearly. I DON'T HAVE a first psionic skills, thereby I have NO way of acquiring psionic skills. I'm asking HOW to get the first psionic skills because... I have a problem on even owning it in the first place. Keep in mind, I already finished the whole game and such, and this is the problem I'm having.
Okay, so you have the Chair next to Oracle in the base, correct? And you are able use it and enter, being able to move between the Red (Melee) Green (Survival) Yellow (Ranged) and purple (Psi) nodes?
(TBH I didn't win a fight, instead I was laying with the girls, till I was 12 hours in, but that is besides the point. )