I was in my Hack & Slash phase when I first saw Dark Sun. Over time, I've learned it's not the "hack'n'slasher's paradise" I once thought of it as.
Anyway, each DS character has a single psionic ability as a natural talent and it's randome. This in no way prevents them from becoming Psionicists during character creation.
Other systems have represented it other ways, for example, Alternity had an optional rule that if you were using the psionics rule, a character not of the Mindwalker profession could choose a single psionic ability as a talent.
I'm not entirely sure this concept would work with the way the HARP psionics system is designed.