Jobs that exist in lore but aren't playable.

[Velaethia]

Here are some I've heard about:

Musketeer: Probably like a pirate/gunner job. Likely too close to Machinist to get added at this point.

Mime: Iirc there is a blue mage carnival npc who is a Mime. Probably won't become playable but would be interesting to have a job that used other job abilities in a specific predetermined way or as a limited job for fun combos.

Mathematician: Clearly a healer. But might be too similar to sage.

Puppetmaster: Melee pet job. No way we're ever getting this as anything besdies a limited job unless they decide to fix how pets work.

Geomancer: Likely a magical support job but could potentially be a healer as well.

Templar: Melee DPS paladin essentially.

Gunhammer: Idk if this job has an official name but it's basically Nero and a few other garleans who use their giant gunhammers. We don't have any hammer jobs yet. It could easily be melee dps or tank.

Any others I forgot to m ention?

[Heroman3003]

Necromancer shows up in one of ShB dungeons. But it's another pet job so highly unlikely.

[TheMightyMollusk]

Thief, necromancer, and berserker show up as bosses in the Heroes' Gauntlet. Thief and berserker are probably too close to rogue/ninja and marauder/warrior to be made as separate jobs, and necromancer is unlikely because pet job (and also some of the countries the game services have laws about depictions of the dead that would probably not gel with it).

Musketeer still has signs up to this day in Limsa around the Marauders' Guild, but with machinist already in game, it would probably be redundant.

Several trust characters have technically unique jobs (G'raha and Venat have all-rounder, Alphinaud has acadamecian pre-Endwalker, Y'shtola's sorcerer, among others), but these are functionally just simplified versions of existing jobs. Scroll down for the list of those.

[Naraku_Diabolos]

Berserker would essentially be a DPS version of WAR.

[Sove92]

Musketeer was originally intended to be a playable class in 1.0, but never made it. That concept eventually evolved into MCH. If SE didn't do away with adding more classes, MSK would have presumably been MCH's base class.

Geomancer is more or less just the Far Eastern take on Conjurer.

One that hasn't been mentioned yet is Void Mage. With the fall of Mhach, the job is extinct and is pretty much the precursor to thaumaturgy.

[AnimaAnimus]

Puppetmaster: Melee pet job. No way we're ever getting this as anything besdies a limited job unless they decide to fix how pets work.

This one makes me sad because pup was one of my favorite jobs in FFXI. But the battle system in XIV with it's strict role adherence and as it was stripped of buffs, debuffs and any interesting stats to manipulate via spells and actions, is way to simplistic for something like this to exist in an interesting way, like it did in XI. What they did with blu, sch and rdm imo are the prime examples of that when you compare them to their XI counterparts, which were some of the best versions of these jobs in the entirety of the franchise. Esp blu.

[Enkidoh]

Thief, Berseker and Necromancer don't count being from another Shard that Elidibus summoned (the Source did have Necromancers, but they were essentially just Void Mages. Berserkers on the Source is really just WAR in every way with a different name, and ROG is literally Thief - Jacke even aludes to it in a comment he made during the early ROG quests).

Apart from MSK, there were a number of other classes in 1.0 that never made it into the game itself or later ARR:

Shepherd (SHP) - a Disciple of the Land that apparently was meant to be some kind of trapper class - it even had a class icon (a pair of deer antlers) and a locked and inaccessable Guildhall in 1.0 Falcon's Nest. Alas, said guildhall was destroyed in the Calamity and it has not been included in the 'rebuilt' Falcon's Nest in HW, it can be assumed to have been abandoned.
Fencer - some kind of Disciple of War melee class using rapiers, dummied out references to 'fencing' skill in 1.0's files hinted at this class. It can be assumed to have served as the foundations for RDM.
Mystic - an apparent Disciple of Magic, again references to 'mysticism' skill dummied out in 1.0's game files hinted at this class. My suspiscions is it served as the basis for AST, but I have no proof of that.
Original ACN - not the version we eventually got in ARR, originally ACN was planned in 1.0 to be something completely different, a Disciple of Magic that wielded weird 'mechanical staves' and used magic-mechanical traps in battle, while using healing skills. Probably was far too mechanically complex to pull off and so was dummied out in 1.0, although several original ACN NPCs showed up in the game, like Urianger (who wielded one such staff - artwork exists of him in this form). Needless to say, ACN was redesigned and repurposed for SMN, being given grimoires and Carbuncle pets instead, losing the staves and traps. Interestingly the staff designs returned in HW, repurposed as the muskets wielded by the gnath/vath in the Dravanian Forelands!
Original BRD - again not the version that was added late in 1.0 piggybacked on ARC, originally BRD was planned to be added to the game wielding musical instruments, but in battle they were to function somewhere between a GLA and a ROG, wielding their musical instruments (specifically flutes and horns) like knives and swords. This was the class Thancred had in 1.0, but in ARR he was changed to being literally a GLA mechanic wise until he was changed to ROG late in ARR's history.

[Dakimakura]

Gunhammer: Idk if this job has an official name but it's basically Nero and a few other garleans who use their giant gunhammers. We don't have any hammer jobs yet. It could easily be melee dps or tank.

I love the idea of a job themed around wielding a big bludgeoning warhammer. I know Warrior is close but axes just don't cut it for me, pun intended.

[CaptainLagbeard]

"Thief" is really just Rogue... The base class for Ninja.
"Geomancer" in XIV is basically a mixture of a little bit Conjurer and mostly AST. Rather than using the stars, they use the earth to essentially do the same stuff.

Necromancy is a thing that exists, but I am of the understanding that it is mildly frowned upon so I don't think we're getting it any time soon.

Musketeer, since Machinist is becoming more and more about using various tools maybe they could make a new Job that focuses on using the gun... They did want to make ranged phys with cast times in HW, I would be fine if they brought it in as a new class rather than forcing existing classes into new playstyles...

[AnimaAnimus]

originally BRD was planned to be added to the game wielding musical instruments, but in battle they were to function somewhere between a GLA and a ROG, wielding their musical instruments (specifically flutes and horns) like knives and swords.

This makes no sense. Why would you beat someone with a clarinet. They could have taken the Edward route with it and made it basically a caster where they played melodies to cause certain effects.

I still hate that the bard we have is basically a ranger. The put way too much emphasis on the bow. Why are dots bow shots instead of songs? Why is the lb a giant rain of arrows instead of something more bard themed? WIth just an ounce of creativity they could do much more with actual bardic elements instead of just reducing everything down to the bow or clubbing things with a flute. Not making bard some sort of song based mage class just makes 0 sense, esp in the context of FF.