Welcome to Flavor Town, where I take things RAW, make no changes mechanically, and yet make a completely new character concept.
Plenty of people do this already but maybe a few who are stuck in a concept rut can find inspiration from this and spice things up. Now, for these articles I'm going to be very strictly rules as written as a proof of concept. As a note, most Dm's are going to be pretty flexible with things like spell components and damage type, but my goal here is to create flavor that can be applied to even the strictest table. That said, I'll usually offer ways to flavor components and Arcane Fouci when they come up. If you DO have a flexible DM, talk to them about thematic changes you may want to make, but remember to be flexible yourself.
As my football coach use to say "Your brain is the muscle that makes your muscles dance!" Now I don't think the brain is a muscle, but he had a whistle on a lanyard so I wasn't going to argue. His point was that the brain controls the body. That's something we are going to need to remember so we don't slam into our suspension of disbelief. Our character IS strong but it is because they have mastered their mind and thus their body. That's all fine and well, but it we want to be a more obviously psionic character we can throw some telekinesis into the pot. After we are done this Barbarian will look a lot more like a Jedi than a wilderness warrior.
So as we know we are using the Barbarian Class, but for race we are gonna use the Githyanki to get that sweet Psionic flavor from the jump. To Further the Flavor (TM) we are going to re-skin this Gith as a human, that way they can fit in any setting. They don't have Darkvision so that's fine, but even if they did we could attribute it to their Psionic abilities. Once we get to level 3 we are going down the path of the Ancestral Guardian. Now that we have our ingredients let's add some seasoning!
A human with Telekinetic abilities that aren't spells is already pretty cool and unique in a fantasy setting, so we have a good start with the Gith's Invisible Mage Hand. Keep in mind that Mage Hand requires Verbal and Somatic components so, baring feats, you need to have a free hand and air needs to pass from your lips with sound. RAW this could be something as simple as a Jedi hand wave an a grunt/hum of effort. Speaking of Jedi, you can use the Jump spell at level 3 to reach people that underestimate your power. Jump needs a material component as well as the others, but there is no reason your Arcane Focus can't be on your crown, as long as you have a free hand to touch it you can try your best Professor X pose and your still within RAW! At 5th level you get Misty Step. Now I don't really associate Psychic powers with teleportation, but hey it's your thing. Personally I like the idea of flavoring that Misty Step as moving faster than observers can see since it is in keeping with our whole "the body does what the mind tells it to" thing. Since the only component is Verbal all you have to do is give your best battle cry, or squeal if you are using it to retreat.
That was just the salt and pepper, now we get to the good stuff. We are going to go down the levels and see how we can flavor each feature.
1. Unarmored Defenses: Why aren't you wearing armor? There are dudes with swords out there! Well why would you wear that uncomfortable, not to mention unfashionable, armor when you could just parry blows with your mind! Mechanically this is just your AC, but whenever an enemy misses you it provides an opportunity for you to describe your character using his Telekinetic abilities to deflect blows that would have otherwise hit. I'm going to call this your " Telekinetic Shield" and it is going to be the bedrock of our flavor. Most of our class features will be flavored as us refining this unique ability. Remember, the mechanics of the game tell you WHAT happened, but you always have the power to describe HOW it happened.
Rage: Ah, the big one. This is actually pretty straight forward. Instead of calling it Rage, call it Focus. When you focus you are channeling your Psionic power directly into your muscles, making them preform beyond what they should be able to, hence the advantage on strength checks/saves, and the shrugging off of physical blows. If you want you can say that your Telekinetic shield is pushing back against weapon attacks, that's why you have resistance to weapon damage. That bonus to damage? Why that is a reflection of your added Telekinetic force to the blow. It is all in how you describe it.
2. Reckless Attack: Remember that Telekinetic Shield? You can re-purpose that telekinetic energy to make your blows faster and catch a nimble target, or apply more force to cut through to an armored target. Careful though, that will leave literally holes in your defense making you more easy to hit! All you are doing is getting advantage in exchange for advantage, and this flavor doesn't change that. Now in a meta sense this flavor doesn't give your enemies a visible cue that you are exposed, but that's a simple fix! Maybe your Telekinetic Shield manifest as some sort of opaque blue or purple shield, and when you use that energy to amplify an attack, it leaves a gap that enemies can see. You can apply this logic to any feature that your DM want to have a visible que for.
3. Ancestral Protectors: I love this feature. It can be flavored as so many different things, it could be a metaphor for techniques taught to you by your family, or a Hex-Blade style haunted sword that enslaves the souls of those you've slain. Today it is being flavored as psionic manipulation. All this feature does is incentivize a target to prioritize attacking you over your ally. That can easily be flavored as reaching out with your mind, consciously or subconsciously. You could reach out with your mind and give the enemy literal tunnel vision, where everything but you is a blur, or we can say that you extend your Unarmored Telekinetic Defense to an ally you see to soften the blow. Maybe the HP lost when your target does manage to hit your friend reflects the stress of seeing an axe blade suspended an inch from their face rather than an actual blow, Thanks Professor X(tra Large)!
6. Spirit Shield: Your ability to use your Telekinetic Shield has merely become more refined. You can now use it to further protect your allies and at greater range. Psimple.
10. Consult the Spirits: Another flavorful nugget of feature! For us though, rather than consulting spirits, we are opening our third eye. We are stretching out with our feelings. My theory is that 99% of the people in the Star Wars universe that utter the words "I have a bad feeling about this" are force sensitive whether they now it or not. This is basically what you are evoking thematically when you cast Augury. Think about your Clairvoyance, rather than an ancestor maybe your sensor looks like how you imagine yourself to be in your own mind, or maybe it is a creepy unblinking eye. This spell should be giving the table even more Professor X vibes.
14. Vengeful Ancestors: You have refined your telekinesis to the point that you not only stop blows from connecting, but actually redirect them. Again, remember that Hit Points are abstract. They could represent injury yes, but they could also represent stress or strain. So maybe you aren't hitting them with their own sword, maybe you are just fatiguing them as they struggle against the weight of your Telekinesis, or you are assaulting their mind directly. Even if a DM won't let you change damage type for balance reasons, you can still flavor your damage as mental.
Other core Class Features: Your other class features show how you are strengthening your mind's control over your own body. Features such as Fast Movement, Relentless Rage, Indomitable Might, and Primal Champion reflect this. They could also reflect how your mind has grown to sense your surroundings jedi style, as shown with Danger Sense and Feral Instinct.
So what we have here as a finished product is a serene character that has harnessed the power of their mind to affect themselves and the world around them. The Sage or Hermit background would serve this concept well, or even an acolyte if your character is from a monastic order. This flavor stands in stark contrast to the flavor presented to us in the PHB or XGTE, but that is part of the fun! Leave a comment about what you think or an example of how YOU would flavor this subclass. Or let this post languish in obscurity, up to you.
This is awesome. I loved reading this and it really inspired me.