Short answer: No psionics.
Long answer: Psionics isn't mentioned in Middle Earth literature, probably because Tolkien didn't think about it.
He wouldn't tell us if something was psionic, since he wasn't using it.
You could probably add it to Middle Earth, as long as you realize it's not in any of the official sources - this means the elven mindlink wouldn't be psionic. (Indeed, don't bother giving elves psionics at all. Not only do they have enough power already, but by DnD tradition they aren't all that good at psionics.)