I was planning in a campaign to feature an NPC, who is actually a metallic dragon that got stuck in human form, this being thanks to a curse that was placed on her.

She is very much wanting this undone, that being intended to serve as a plot hook/lead-in for some events which are planned to occur.

But, to make sure first before I go ahead, is there any actual way for this to have even been done in the first place: an adult dragon made stuck in a polymorphed form and prevented from turning back into their true one?

Or would it be impossible for such a thing to have been done to a dragon?

Sure, You're the DM.

If you want there to be a Curse that has entrapped a Dragon in Human Form, then you can invent one. There is no need for RAW to support this--creating curses-as-plot-devices is entirely within your purview as the DM.

However, there are some things to consider...similar things have come up in games I've designed when adding in extra effects as a DM

How did the curse happen?

Did the dragon come upon a cursed artifact? Were they cursed by some powerful magical ritual? Did a powerful mage hit them with a Bestow Curse that disabled their Shapechange? Did they tick off Bahamut and he cursed them to be stuck as a human? Did they get hit with True Polymorph (not Shapechange...but still puts them in human form)?

Why are they still cursed?

If you're dealing with an adult dragon, they are phenomenally wealthy. If you're dealing with an ordinary curse, it can be broken with the 3rd level spell Remove Curse. Breaking a normal curse would simply be a matter of the dragon finding someone who could cast Remove Curse, then throwing gold at them until they did so without asking any questions.

Even a True Polymorph can be broken with 3rd level Dispel Magic and an excellent Spellcasting Check...meaning the dragon would just have to pay someone to keep trying until they pulled it off.

That said, as the DM, you are free to invent new concepts and add them to the world as you wish. If you want this to be a particularly potent curse that requires an Upcast (cast with a higher level spell slot) Remove Curse to break--you can do so...this increases how hard it is for the dragon to find someone able to break the curse--especially while limited by their ability to move around.

You could also make it that Remove Curse simply doesn't work on this. There is some other condition that must be met to break the curse...perhaps they have to find the other half of some artifact, perhaps they have to kill the person who placed the curse, or Bahamut cursed them to learn some humility and they are stuck that way until they come to understand/respect humanity, or some other condition is applied.

Or, perhaps the dragon got stuck in human form a long, long way from civilization and simply hasn't been able to travel far enough as a human to get somewhere with a sufficiently powerful spellcaster. Or they can't actually get to their hoard without the ability to fly -- so they haven't been able to actually go get the money they'd need to pay someone to uncurse them.

There are many 'problems' that we, as DMs, think of that have very simple solutions. So you'll need to think of why the Dragon has not been able to be rid of this curse. If you want it to be more complicated than 'Pop Remove Curse,' then you could even lampshade it a bit--have the dragon remark "You think I didn't try that already?"

Yes

Don't worry about the details, just make it happen

As the DM you have full control over your game-world, so you don't need to find an excuse to have your dragon stuck, you can just make up a curse that does what you want it to. The game is just a game, and you're in charge of the rules, so you can make them what you need.

RAW

The spell True Polymorph can accomplish this. The spell states:

The target's game statistics, including mental ability scores, are replaced by the statistics of the new form. It retains its alignment and personality.

The Change Shape action of dragons is one of the statistics that gets replaced, so the dragon would be stuck until the spell is removed.