After setting up some basic principles and restrictions, writing up a few abilities, and testing them out on my players recently, I can say with confidence, no, certainty, that I know how psionics can and should be done in 5E.
First thing I want to note is the fact psionics should not be a default feature of D&D. I certainly think if I was a designer on D&D, I would designate specific domains psionics would be used for (and would therefore not appear in abilities like spells) in anticipation for settings psionics prominently featured in. I would have done this, seeing as though earlier editions of my games had settings which included psionics, and would try to ensure that any eventual inclusion of psionics would not step on the toes of other features of the game. This is commonly known as “foresight”, and we know not to expect such things from WOTC. Certainly, I would never include items which were previously psionics as spells in add-ons to the game 4 years in when people were clamoring for psionics.
I’m inclined to agree with the OSR guys that Monk shouldn’t be a default D&D class. Why? Because it’s a psionic class. It has supernatural abilities that are often not interpreted as being magic (and existing within systems of magic), though they can certainly interact with magic. Point being, you should explain why supernatural effects not covered by magic exist in your game, both in a narrative and mechanical sense. That explanation can be as simple as “It’s always been here, no one’s bothered to look into it. We just know the things we do with magic and the things we do with this other thing are different.” Not the coolest explanation in the world, but hell, you’re busy. We get it.
Before I give you my explanation, let’s switch to the mechanical purpose of the system. In spite of previously existing spells and abilities, we have options insofar as what domains psionics cover. Whereas spells displace a person’s personality, psionics make minute adjsutments to their personality. You can flavor this as attacking the conscious vs subconscious mind. A suggestion spell may force you to run away from a battle, whereas a similar psionic might impart you with a phobia (of say, metal) to achieve a potentially similar but unique effect.
Here’s another; spells conjure matter and energy, generally do so for specific effects, rather than to be manipulated themselves. Those instances in which they do wouldn’t be present in a system designed from the ground up with psionics in mind, but such things fall to me to do. Psionics on the other hand manipulate matter, whether conjured or present naturally. What do I mean by manipulate? I can hardly think of a better example than Avatar: The Last Airbender (which I only recently watched for the first time). There’s a potential exception when it comes to firebending, but that’s neither here nor there. The primary focus is in manipulating the elements present to your whim, not spontaneously creating or summoning them. You turn water to ice, raise walls of stone, move objects by bending their air around them, etc, This system is potentially more open to creativity than spellcasting generally is, but that’s a double edged sword we’ll have to blunt when it comes to restrictions in a moment.
One other comparison, before we do. There’s only one spell that explicitly affects time in 5e as it currently stands, and that’s Time Stop. It’s quite garbage without some changes to the Concentration mechanic, but we’ll leave that to the side (much as I enjoy screeching about it). Other spells like Haste and Slow obviously invoke thoughts of time in the name, but can be thought of as affecting processes other than time itself ( internal chemistry, creature’s perception, etc). Psionics of a similar sort would affect actual time, displacing a creature for 3 rounds, for instance. They might reverse a creature’s wounds! Said reversal would be more or less powerful based on the most recent damage the creature took, and indeed, that’d be your balance factor for such an ability.
So, let’s run over the comparisons again:
Displacing Personality vs Manipulating Subconscious
Conjuring Matter vs Manipulating Matter
Enhancing Creatures vs Altering Time
Let’s talk restrictions. Psionics are primarily based off the mind, and by extension, their senses. Spells can be fairly loose with what does or does not allow you to target creatures with them. Psionics need restrictions based on said perceptions built into the abilities, given a lack of common counters that magic has (counterspell, magic resistance, generic anti-magic fields, etc). I’ll develop comparable counters at some point, but that only comes after the system’s creation. Maybe not, I’ve already thought of a few as I type this. I can’t help it though, I’m just too creative. So what I’ll say as general advice is plan ahead, but don’t leap to the “ahead” portion until you’ve squared everything you need to make the system function away. Back to the point; psionics need restrictions baked into the system. “A target you can see” is my go-to, and allows enemies with the proper gear or tactical acumen to defend against sight-based spells. Ditto for psionics. Certainly one could think of higher level psionics not having restrictions on sight, but rather “At a point of which you’re aware” or some similar language, to ease the burden on the sense and reflect the Seer’s improving skills.
What we should probably develop next are general classifications of psionic abilities, much like spells have schools. We’ll take a note from the Mystic UA here and call them disciplines. Chronos will denote our time-based abilities. Telekinetics will cover abilities that manipulate matter. Cognetics will be our mind-altering subst-I mean abilities. I’m going to include another here (mostly for my own records) called Fractures, where reality writ-large is adjusted in one way or another, sort of a catch-all for things not covered in the others.
These are just examples to spin off of, general principles to use as you generated psionic abilities. You will inevitably step on the toes of spellcasting or other abilities, that’s fine. As long as the majority of the system feels as if it’s tackling problems from a different angle, the exceptions won’t ruin the fantasy.
Speaking of the fantasy, let’s talk narrative. Mine, in particular.
Psionics in my world come from the Nightmare. They’re able to pick and choose pieces of this unreality mirroring their own, and displace one another. As they get stronger, they begin matching the divinity that spawned the Nightmare to begin with, and exercise a finer control over what gets displaced (manipulating the Nightmare itself before taking pieces of it). This process isn’t entirely conscious; the psions (Seers, on Brackas) know what effects they’ll produce, but not entirely how its done. In some sense, they guard themselves against knowing; woe to the inexperienced Seer who gazes to far into whatever window is opened by their psionics. You never know what gazes back.
Given that lovecrafty things have a very specific explanation for their existence, and have fleshed out consequences and counter-consequences for their coming into being, psions (as created in Brackas) make quite a bit of sense! That’s not the case in all settings, and if i’s not the case in yours, knead an explanation into it (perhaps by changing/advancing the world state), or don’t include it. It’ll feel weird, and forced. Probably.