I know he was supposed to be “dead dead” after Wrath of the Lich King, but with his appearance in SL, and him being a lich and all I could definitely see him trying to return to the mortal world
Maybe now that the veil is shattered?
Will we see more of him?
I dunno. Probably not. There’s only so many times the same villains can come back over and over. We really begin to super devalue death if we just keep bringing back people who died over and over. Which is an unfortunate plot device Blizzard overuses in my opinion.
No he’s dead dead now. We destroyed his phylactery this time, unlike Wrath, and every trace of his spirit in the Sanctum raid. Souls who die again in the SL have a true death and no longer exist. Anima to the wind.
So Kel’thuzad’s character is done, he’s not coming back.
If the phylactery is destroyed then he’s gone for good. Even the liches in Maldraxxus can come back if they got their phylactery. Well according to Draka anyway.
So what makes him different than the other souls in maldraxxus that can just get a new body when they die?
Maybe once you become a lich that’s not possible anymore? 
He’s still a lich even in maldraxxus so with his phylactery destroyed he can’t come back.
He wasn’t one of the souls used in a construct. Those can just get into a new construct body once they can get one.
He was never supposed to be “dead dead” after his loss in Wrath. No idea why you would think so.
As for Kel’thuzad in the future, he is dead. We destroy his Phylactery in his encounter in SoD then we kill him once and for all.
And it is a shame that blizzard character assassinated him by making it so that he was serving Zovaal from the very beginning of his fall from grace. Even before he met Ner’zhul before the events of WC3.
I guess new blizzard will do anything to boost Zovaals “big villain vibes” without giving him an actual character. Who needs that when you got retcons galore.
It is hinted that after his resurrection shortly before Wrath, he hid his phylactery in the shadowlands. So when he “died” in Wrath, he spawned there. As an answer to your second question, yes that is what happens according to the Kyrian WQ Limbo. When a lich from the mortal plane has their phylactery destroyed, and they die afterwards, they will go to the Shadowlands. This is most likely why Kel’thuzad put his phylactery in the Shadowlands to avoid the soul sorting robot from sending him to the wrong realm if we ever found it and destroyed it during Wrath. However as a consequence, it would seem that doing so bound his soul to the shadowlands. So when we do defeat him in the raid, he is gone for good.
A lich in Maldraxxus using a phylactery is basically a safety net so when they die, they don’t get turned into anima for good. Destroying the phylactery removes that safety net.
But why would a phylactery be taken from the real world into the afterlife?
Isn’t entering the afterlife what happens when their phylactery is destroyed?
I’m just really confused on how a lich follows all the same rules in the afterlife as they do in real life
Lemme check the “lore” with liches here brb
Edit:
Unlike many other forms of undead, a lich’s soul is not imperfectly attached to its body; instead, liches bind their souls to special containers known as phylacteries, which then allows them to generate a physical form. This is why lich bodies look nothing like their former mortal selves, and also why one has to destroy a lich’s phylactery to truly kill them; as long as a lich’s phylactery and soul are allowed to remain intact, the being can never truly die and will always be able to regenerate their corporeal body.
Maldraxxus is the birthplace of necromantic magic and home to the forces that were called upon by the Lich King and the Scourge on Azeroth. The House of Rituals is lead by necromancers and liches, and are constantly innovating and advancing the art of necromancy with new incantations and formulae as well as more resilient phylacteries.
I hope not. Let the dead stay dead.
Ooooh I did not know this
Well that explains why he has it here then. I guess he’s really gone then 
Sad, he’s my favorite villain
Naw I think he’s gone gone this time.
Blizzard have been on a hot mission since Legion to finish all the loose ends of the old-school lore. From the mysteries the artifacts resolved (What’s beneath Tirisfal / Scythe of Elune etc.) to Sargeras and Argus to N’zoth, Azshara and Nazjatar, now in Shadowlands we’re resolving the mysteries surrounding the Lich King etc. Practically all old lore mysteries from the WC3 era are pretty much done. So that includes Kel’thuzad. All we got going forward is new era lore such as The Void Lords and perhaps the Elune revelations. New age Warcraft.
I always felt like Kel’thuzad had the potential to be his own big story villain if he wanted to. Or at the least try to Death and Decay bomb Stormwind during a ghoul rush.
As much as I think death should be impactful in the series, I also feel like Blizzard likes to treat villains a bit too expendable for a long-term MMO story. There’s a reason it took Ash Ketchum 22 years to become a Pokemon Master in the anime (though that could be a case for hanging onto something far too long, too). We wouldn’t have Zovaal in the first place if we didn’t kill off everything in their respective expansions, sometimes just thwarting their plans and putting them on hiatus is enough.
Kel’thuzad: Friendship ended with the Lich King. Now Zovaal is my new best friend.
Why are so many people asking if we will see characters again who have died in the Shadowlands? How is this unclear… Guys… Garrosh is gone… KT is gone…
Until we go back in time. 
Or an alternate timeline
Non-controversial option: KT should get the redemption not fail wail.
Not again.
I expect they may do something with the Nerubians next. They were the big baddies in Northrend before Kel’Thuzad showed up, and now that tons of undead Nerubians have their free will back they’ll probably be rebuilding their empire and giving necromancy a serious gander.