Ok, so basically a fight against an aberration went south for a PC last session and now the party has a brainless corpse and a brain in a jar , the player who's PC died and I have come up with an idea that the party can take the corpse and the brain to someone to "Frankenstein it up" so the player can come back as a new class in the old body (think freaky Friday or something along those lines)

I have ideas for a mad scientist type character to perform the operation but I'm struggling for ideas in what they would want in exchange. The party is only level 5 and don't have a lot of resources at their disposal right now and I'd ideally like to have the player come back sooner rather than later so they don't have to sit at the table watching everyone else play while they wait for the operation to be completed.

Something along the lines of "I'll fix your friend but you have to go and do X afterwards"

Many thanks in advance 

Recover an Arcane object from a dungeon/temple/cult

steal an item from a rival, plant false evidence to discredit rival

capture a creature/monster/tiefling/other monstrous species, so that “experiments” can be done or essence extracted

Meteorite iron and hair from the mane of a black unicorn (they could bargain with the uni for the hair) 

the heart of a young black dragon 

take an item somewhere and activate it so the scientist can witness the experiment from a safe place 

but they need a reason to return - some homebrew of soul coin or soul cage

Well, for one thing it's not a True Resurrection if you have a body part left, just a straight Resurrection. That's not just me being finicky about semantics; the kind of being who can cast or replicate the effect of a 9th level spell is at least an order of magnitude stronger than one who can only do 7th level, within the typical D&D power scale. That said, this is still going to be someone who might not find much use for a low 2nd tier party; if you just want to handwave it you can always just play the "you'll repay me, one day..." bit and keep that marker in your back pocket to work into a later plot point. Alternatively, you could try the "domino effect" bit; the party is tasked with something small and innocuous, but they learn it set off a larger chain of events. Would be another good way to set a plot hook if they're tied to those events in some way.

A mad scientist would likely want help that would further their research/experiments/boost reputation so the options Stavros gives sound fun and like they would fit narratively. You could modify a 5th or 6th level adventure to fit your needs. 

Another route you could take is less directly related to research and more toward other plot tropes that have a mad science twist. The scientist might be feeling unrequited love and ask the party to get ingredients for a love potion or have the party diplomatically approach a love interest. The mad scientist might want to become town mayor and if you help, then your party would be responsible for helping to found a mad science town for good or bad. 

If you want to, you could have the scientist hold the "Frankensteined" character hostage (the patient will disintegrate in X days unless I receive the necessary materials) to direct the party to participate in a mad science adventure.

There are plenty of fun routes you can take to satisfy your mad scientist. It is up to you to decide how much time you want your party to dedicate to this task, as well as decide what lasting consequences of this interaction.

Another option to help the player whose PC is dead, maybe let them play a temporary character while they go on this quest. Perhaps the mad scientist has an assistant that he will send with the party, whom your player could create and play. My DM did something similar for me when my PC was killed, and the rest of the party had to collect the resurrection material for the town cleric, and while he was recovering.

How serious do you want to be? I’m picturing a mad scientist whose mind constantly flits from one thing to another. They might ask the party to retrieve some obscure ingredients for their next experiment, or if you catch them at lunchtime, they might want a really good sandwich. 

If the idea is that they're coming back with a new class, the mad scientist might just want to be allowed to use some sort of experimental gizmo on the body that alters it somehow, resulting in the class change.

Alternatively or in addition, they may just have the party owe them a favor to be called in at a later date (in other words, once the party is higher level).

If he's really mad, roll 50/50 between something absurdly common - like an omelette with bacon and tomatoes - or something absurdly uncommon like a dragon egg.

Reincarnate is always an interesting spell to use in this kind of situation.

Yeah, reincarnate is the lowest level option that fixes the problem. However, given that you have both a brain in a jar and a brainless body, you could always come up with a mad science solution instead of any conventional spell (probably turning the character into a construct-type Reborn). In that case, the character is an 'experimental test subject' and the mad scientist probably wants reports on how the process is going.

It's the perfect chance to, ah, resurrect his old project which has been at a standstill for years. His goal was, and is, to create a form of life that can... Digest rocks! Get hit with lightning and turn the energy into nutrients! Survive a 60ft sheer drop! Frighten an owlbear! And many more moderately dangerous tasks! When he can prove his creation is capable of these things, he can finally join the academy or whatever.

If you need to give them a strong reason to do these things aside from obligation or curiosity, you could make it so the character needs maintenance of some kind, that only the scientist can provide.

maybe the mad doc has a device which can communicate with a soul on the ethereal plane which is convenient because he has some things in the ethereal plane that he requires be shuffled about. maybe something smuggled in past a sort of ethereal blockade that's formed around his lab by angry spirits. you can even work up an encounter that requires the party to wield strange inventions to assist him: oversized electric fly swats that can block spirits, spare reinforced curtains which two persons could use to cover 'holes' in the lab's defense lest poltergeists slip in and put on the professor's Ghost Gloves of Material Punching, goggles for some and large two-handed magic mirrors for others (and a challenge to coordinate perception or solve a mirror-laser-mirror puzzle), nebulous port-holes that must be covered as strange arms reach out to hinder characters, a summoning ring fires up on it's own and random beasts begin to appear to chaotic effect, etc etc.

(inspiration roughly from Rime of the Frostmaiden Ch2)

Quote from Acromos >>

If he's really mad, roll 50/50 between something absurdly common - like an omelette with bacon and tomatoes - or something absurdly uncommon like a dragon egg.

 Dragon egg omlette, with a yellow musk creeper salad, and elephant cheese.