Yes, and this continuity would be a NEW version of the prime universe.
A 'new version of the prime universe' is by definition not the prime universe.
A 'new version' of something is not the same thing, pretty much by nature.
A new version of a universe, is a new universe. Two different things cannot simultaneously be the same thing - that is a logical fallacy. Call it universe one, and universe two, but they cannot both be universe one.
Let's assume you are using imprecise language. Maybe you mean to say 'a new redition of the story', like a different Shakespeare company's rendition of Richard III. First, when performing the play, they are not adapting a 'new version of Shakespeare's play' - the lines are all exactly the same. But second, and more importantly, it still does not make sense, since a new rendition of Star Trek, would be a new universe - actually, each performance of Richard III is basically a reboot, implicitly set in a new universe, if you want to apply geek franchise rules.
Fictional film, television and video game settings are not stage plays, to begin with. The sets don't get changed from week to week on a whim as a new set of performers walk in. Come to think of it, even comic books usually mandate that a different visual interpretation of an existing character is a new universe entirely. So even an industry born in the 1930s and 1940s notorious for it's lack of consistency, and originally written for pre-teen kids, has more coherence than your view of what a visual change means for a universe - the Animated Series Batman is not meant to be the same Batman as Adam West's - even Marvel mostly makes each visual adaptation a new quantum reality, like Earth-616, Earth-199999, even when their continuity does not implicitly conflict.
Star Trek has a very long history of what is considered continuity, and I frankly don't want to see it ape some in-vogue post-modern nonsense, just because it's fashionable to be 'meta' with fiction. Your attempt to retool Star Trek's definition of a universe notwithstanding, Star Trek has had very clear and simple policy - it's definition of universe is the scientific one, not an entertainment industry one; a new universe literally cannot occupy the same space - it is mutually exclusive - if history it altered, and the alteration wasn't pre-destination, it's a new timeline.
We accept re-casting of characters, etc, because we know that in real life, you can't always get the same actors back, but other than minor facets of the medium like that, Star Trek has maintained itself as a consistent setting for 50 years - the Klingon battle-cruiser in 1979's Motion Picture is almost identical in shape to the TOS one from 1968, so fans can easily see it's extra detailing as a refit or something - Mr Scott even has a line about how the Enterprise has been rebuilt.
Your idea of what the 'new prime timeline' is, amounts to sophistry. Say that one day a new Star Trek show was made, and it was a reboot. They shouldn't employ Orwellian doublespeak to basically try to have it both ways (it both is a reboot and isn't). They shouldn't try to capitalize on the notion of a prequel, whilst ignoring any responsibility that a prequel brings. You can be very creative, whilst also being smart enough that the changes don't conflict. But if you are not willing to do that, or have a creative vision you want to fulfill separate from it, just be honest, and announce a reboot.

Let's discuss what Star Trek has done until now: In Star Trek, there are terms like 'timeline', 'universe' and 'dimension'. Sometimes they are confused by viewers, who may be used to other franchises applying these real world physics terms incorrectly. Star Trek is however usually quite consistent, let's look at them: 1). A dimension is a higher or lower dimension in 'string theory' and 'M theory' interpretations of spacetime; it has no relation to timelines or universes, and can be ignored. 2). A timeline/universe/reality (all interchangeable terms) is a branch of how history/causality unfolded, which creates a new universe, as Star Trek follows the 'many worlds' interpretation of quantum physics, where for each possible outcome of an event there is a different quantum reality. Thus, in Star Trek, the Mirror Universe, Kelvin Timeline, and reality seen in Yesterday's Enterprise, are all examples of parallel universes within the many worlds interpretation of cosmology. They are not reboots, as they are all equally legitimate twins of the prime universe, and exist contemporary to it. Star Trek has never had a reboot - but a timeline may practically function as one for the purpose of real-life writing, as the Kelvin timeline does. It's not a reboot - i.e. Battlestar Galactica 2004 was a reboot of Battlestar Galactica 1978. This is the most commonly accepted definition of reboot; a brand new version of a setting, before studios started using 'reboot' to mean just 'revive'. Star Wars has also never had a reboot, nor have Babylon 5, Farscape, Firefly, Mass Effect, Warhammer 40000, Halo, or any number of science fiction franchises. To reboot JRR Tolkien's legendarium, would be tantamount to cultural vandalism; the carefully crafted setting's intricate continuity is a masterpiece and essential to it's value. It is something relatively novel outside of comic book films and the like, because they never had any standard of continuity to begin with.
1968, the Klingon battlecruiser:

1979, the higher detailed Klingon battlecruiser:

1987-2001, the Klingon battlecruiser is used in TNG, DS9, VOY and ENT:

2009, the Kelvin timeline's battlecruiser:

We fully understand your view. You want to start treating each in-universe 'timeline' (Prime, Mirror, Kelvin, etc) as something that can be ignored by a new company of graphics designers whenever it suits people - you want it to somehow officially remain the 'same universe'. To some extent this happens in some other visual media and franchises. In Marvel's Earth-616 reality, new artists re-interpret things - nobody has aged since the 1960s, and people who were alive during The Bay of Pigs Invasion are somehow still 30 years old when 9/11 happens - no explanation is given. I would argue Earth-616 makes no sense, for this reason, is actually clearly a series of realities, and falls apart logically as a single setting. This is a completely different culture, more similar to a Homeric poet retelling the Trojan War differently to different villages, than to a beloved and consistent space opera franchise like Star Trek. Please stop trying to foist comics book culture onto a space opera with a grand history of it's own. People have enjoyed reading and writing Encyclopedias and Concordances for 50 years, and I object to Star Trek lowering its standards, to the point it would damage the value of the property. Just make it a full reboot, or else don't reboot it.
One day, I think Star Trek might get a full reboot. Right now it essentially has two settings, which supposedly have a shared history up until 2233 A.D. Until Discovery is clarified otherwise, it is a part of prime's universe's history and causality, and that comes with responsibilities. Klingon battlecruisers must be built from the same blueprints, designed by the same person, in the same way, as they were any previous time we saw them, and thus must look reasonably like a refit or newer model of the same vessel.
Reboots do not create alternate timelines, that's just not how that works. Reboots go back to a point in the existing timeline and retell the entire story from that point, erasing everything that came after and most of what came before.
Well, if you say "that's just not how it works", I guess I'll just stop using my own mind to reach my own conclusions.
You know, the main reason why this debate is still going on is simply that people in entertainment circles have muddied the waters with imprecise sophist language - where 'reboot' once had one definition, which meant 'making an all-new version of a given piece of entertainment, bearing only basic relationship', Hollywood executives have introduced weasel words - I can barely write this post without using these false terms for things, because they have become so prevalent.
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