I am running a session and one of the players who was already in our group invited another player into the game, however the newcomer wants to be some sort of plant creature however I am unsure if that even exists and if not what could I do to make one?

Not sure if there is something like that for PC, I would allow for something like dryad, or potentially treant (preferably young one that does not have the size of a huge tree yet). You might need to home brew the characteristics of the plant based PC creature.

I don’t believe there are any official plant creatures. 
I’d suggest re-skinning one of the existing races. That works for most stuff.
In particular, I’d make sure the creature type stays humanoid. Maybe fey. Just know there’s some funky rules interactions if they’re not humanoid with some spells that only target humanoids.  

I'd either roll with a re-skinned Warforged, or go with Tasha's Custom Lineages and replace the free feat with gaining Find Familiar and Thorn Whip at 1st level and Flock of Familiars at 3rd level.

Well, you could pretty easily homebrew something like that, if you don't mind homebrewing. Like maybe the character was a twig blight or a needle blight that was somehow awakened and turned non-evil. Or maybe they're a little sapling who will grow into a treant in a century or so. Aaanyhow...

You could call it a Twigling. Medium size. 30' movement. Ability score adjustment +2 to one, +1 to another. They speak Common and Sylvan. They have an unarmored AC of 13 due to their tough bark-like "skin". They know the cantrips Druidcraft and either Shillelagh or Thorn Whip (their choice). At level 5 they will be able to cast Speak With Plants once per day without using a spell slot. And they have the Mask of the Wild ability, allowing them to use an action to hide in a natural setting (because they look like a plant).

But! They have vulnerability to fire damage! And the Blight spell always does full damage against them, because they are a plant. 

Boom. Easy. Twigling. 

Another plant creature you could homebrew would be a myconid. That might be easier to make than some other creatures as there's lots of information.

You could also let them play an awakened plant

https://www.dndbeyond.com/homebrew/races?filter-name=myconid&filter-author=&filter-author-previous=&filter-author-symbol=&filter-rating=-14 

There are a lot of homebrew myconids that people have created there ^. Perhaps, you'll find one that suits what you're looking for. Alternatively, if you're willing to trawl through it, looking up plant will get you other options.

Hope this helps. 

You could make a dryad-inspired or blight-inspired race. Their size could be Medium or Small. Make them speak Druidic or Sylvan.

Groot? Groot!

First:
You ask why they want to play a plant, what are they using for inspiration, and what kinds of abilities they are envisioning. 

Just giving a PC a bunch of spells/abilities that exist in d&d because they happen to be plant flavored is not a great way of going about this because other than "plant" you don't have any idea if you are helping craft a character the player actually wants to play.

There's a nice plantlike race "Wilden" described in Race Compendium - Volume One. (Dungeon Masters Guild)

Reskin the Firbolg as some kind of large plant like creature. 

I think that gets pretty darn close. 

Forest Gnome is a close second. 

Check out the leshy from Pathfinder 2e

Leshy's were a race once? That's cool.

There are vegepygmies, young treants, dryads, myconids, blights, wood woads, (you could let them become one if they play a druid)and you could easily homebrew one based off of vampiric vegetables. They are a legitimate thing, I didn't make them up.

Warforged are plant-based according to standard lore. Their cores are made of woody vines. Only their outsides are metal. You can either lean in to the plant nature of warforged or lean into their machine nature, or both.

I played a re-themed warforged druid with stone outer plating instead of metal, and I played them more like an ent than a terminator, although my character's name was Timminator.

Quote from AnzioFaro >>

Well, you could pretty easily homebrew something like that, if you don't mind homebrewing. Like maybe the character was a twig blight or a needle blight that was somehow awakened and turned non-evil. Or maybe they're a little sapling who will grow into a treant in a century or so. Aaanyhow...

You could call it a Twigling. Medium size. 30' movement. Ability score adjustment +2 to one, +1 to another. They speak Common and Sylvan. They have an unarmored AC of 13 due to their tough bark-like "skin". They know the cantrips Druidcraft and either Shillelagh or Thorn Whip (their choice). At level 5 they will be able to cast Speak With Plants once per day without using a spell slot. And they have the Mask of the Wild ability, allowing them to use an action to hide in a natural setting (because they look like a plant).

But! They have vulnerability to fire damage! And the Blight spell always does full damage against them, because they are a plant. 

Boom. Easy. Twigling. 

 Cool ideas. However, I'd remove the vulnerability to fire. It is far too much of a liability for a playable race (16d6 fireball damage). Removing it can also be justified to some extent because fresh wood doesn't burn well.

The OP could also include some effects due to their plant based nature. Doesn't need to eat. Needs to be rooted in soil for at least 4 hours/day. If they are a succulent then water requirements can be reduced. Require something like at least 8 hours of sunlight/week. The character is aware during a long rest. Rooting requires an action to start or stop.

I found this a while ago and remade it for my games, They are basically playable ents, they have three subraces

Arbrekins

I had an idea for a character - a reborn lineage circle of spores druid.  The idea was basically ripping off Swamp Thing - the character was a man who had been killed and broken down by fungi.  The fungi gained some of his memories, but he would basically be a plant creature.

Make something like Groot!

A wood elf  as a kind of plant elf.  If you want to make minor modifications you could:

• Change the language from elvish to druidic  or the firbolg speak with animals and plants trait
• Replace the weapon training with a racial spell casting trait with druid or range spells themed spells. ( modern races get a cantrip + once a day 1st level at level 3 and  once a day 2nd level at level 5)

 Another option is modifying the firbolg . If you want modifications:

• replace hidden step with mask of the wild or similarly plant themed hiding ability 
• change the language to druidic
• replace the spells of firbolg magic with druidic or ranger spells based on plants 
• replace firbolg magic with a general racial spell casting trait. ( modern races get a cantrip + once a day 1st level at level 3 and  once a day 2nd level at level 5)

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