So I'm thinking of a few adventure hooks for my players, and I thought about the possibility of them removing a demon that has possessed a noble. Are there currently any mechanics or rules surrounding possession and the removal of entities?
If not, does anyone have any play-tested homebrew rules?
The rules don't really specify what happens when a demonic spirit is exorcised, so we're going to be using the assumption that the spirit is still around once it leaves the body. If you rule differently, you won't need the latter half of this answer.
Dispel Evil and Good explicitly mentions ending possession of a creature. This will probably be the easiest way to get the demon out.
Break Enchantment: As your action, you touch a creature you can reach that is charmed, frightened, or possessed by a celestial, an elemental, a fey, a fiend, or an undead. The creature you touch is no longer charmed, frightened, or possessed by such creatures. (PHB, 233-234)
What is told about demonic possession from the Monster Manual is that demons can possess creatures when their essence emerges from the container that holds it, which implies the demon was bound to an object. Essence here implies more of a spirit or soul, rather than tangible body. You can read about binding demons and possession in the Monster Manual, page 51, under the headers Bound Demons and Demonic Possession. This also suggests that demons can't normally possess other creatures if they have their own tangible body. There's nothing to suggest their spirit can move from body to body willingly, but there's nothing suggesting they can't possess another creature after their spirit has forcefully been removed from the previous host either.
What this likely means is that exercising the demon will probably result in it attempting to possess another creature.
You have two options:
With this option, you're looking to send the demon spirit away. If the DM allows it, the spirit should be able to be targeted by spells. There's no real rules for a spirit, so you'll need to decide if this is possible. If it is you can use a simple spell like Banishment to send the spirit back. Another, more complicated way is to cast True Resurrection on the spirit (you'll need to know his true name) and then fight its new body to send it back. You may also use that as a bargaining chip, to perhaps make a deal with the demon, if that is even possible.
You might also be able to remove the demon by finding an amulet it has put part of its essence into. Destroying the amulet will trap the demon in the Abyss for a year and a day (MM, pg 51, Protected Essence). This would probably end possession and send it back all in one go, depending on how you rule it.
You also have the option to bind the Demon to an object, which is likely how it came to possess something in the first place.
The Monster Manual suggests that The Book of Vile Darkness, the Black Scrolls of Ahm, and the Demonomicon of Iggwilv are the foremost authorities on this subject. The Book of Vile Darkness is detailed in the Dungeon Master's Guide on page 222, in the Artifacts section. Suffice it to say that binding the demonic essence or sending it back to the Abyss is something you're going to have to use your DM powers for. Keep in mind you'll most likely need an evil character to use the book. The Book of Exalted Deeds is basically the polar opposite of this and might also help, altough it doesn't detail any control over fiends and the like, but it does help you fight them and can even destroy an evil creature that tries to read it (if a demon, this would likely send it back to the Abyss).
It would be smart to cast Protection from Evil and Good on your party and any participants in the exorcism, as it protects you from possession. It can also be used to exorcise the demon from the host, but only if there is a relevant save (there isn't one listed for demonic possession).
I'd also suggest a good reason for the possession. The MM suggests that demons that escape their bindings seek revenge on the one who bound them, which could be the noble or someone close to him, depending on how powerful the demon is. Greater demons are usually smarter than lesser demons - I mean that to say that a greater demon would likely plot and scheme through possession, where a lesser demon would likely just rage around and create chaos.
The new spell I wanted to bring to this Q&A is the hallow spell. This spell includes the following with regards to ending possession (PHB, p. 249):
You touch a point and infuse an area around it with holy (or unholy) power. The area can have a radius up to 60 feet, and the spell fails if the radius includes an area already under the effect a hallow spell. The affected area is subject to the following effects.
First, celestials, elementals, fey, fiends, and undead can't enter the area, nor can such creatures charm, frighten, or possess creatures within it. Any creature charmed, frightened, or possessed by such a creature is no longer charmed, frightened, or possessed upon entering the area. [...]
So, assuming your hallowed ground affects the type of creature possessing you (undead for ghosts, fiend for demons, etc), then upon the possessed creature entering the area, the creature is no longer possessed, implies that they are forced out of the creature and stuck on the outside of the area whilst their previous target can remain within the area.
If the ghost/demon/etc wants to then try to possess another creature, then if any other possible targets within range are also within the hallowed ground, the ghost/demon/etc cannot possess another target.
As has been mentioned in Premier Bromanov's answer, dispel evil and good explicitly mentions ending possession of a creature (PHB, pp. 33-234):
Break Enchantment. As your action, you touch a creature you can reach that is charmed, frightened, or possessed by a celestial, an elemental, a fey, a fiend, or an undead. The creature you touch is no longer charmed, frightened, or possessed by such creatures.
And, of course, protection from evil and good can prevent you from getting possessed in the first place, and is the only spell here that is below a 5th level spell, but it requires knowing about the possibility of possession beforehand (PHB, p. 270):
Until the spell ends, one willing creature you touch is protected against certain types of creatures: aberrations, celestials, elementals, fey, fiends, and undead.
The protection grants several benefits. Creatures of those types have disadvantage on attack rolls against the target. The target also can't be charmed, frightened, or possessed by them. If the target is already charmed, frightened, or possessed by such a creature, the target has advantage on any new saving throw against the relevant effect.
Looking at options for lower level characters I think Magic Circle (3rd level Cleric/Paladin spell) could be used to dispossess a character or creature if the Magic Circle could be drawn around the possessed somehow or if the possessed creature could be physically pulled into the Circle it could force a dispossession.
