Get clear coat spray. Test a little in a spot that isn't visible to make sure it doesn't react with the surface negatively. Spray some onto cloth that won't leave behind fibers or you'll be sad, then wipe a little on a corner and make sure the material and surface coloring don't react or run.

After you've let it dry, check it.

Hang it from a wire or something so you can get all sides in one pass.

Spray clear coat LIGHTLY.

Like... SUPER LIGHTLY. One small pass. Let it dry. Spray from about 6-8 inches from the clip and move your hand in one direction smoothly... left to right or whatever. Don't do the hairspray thing where you're just dousing it.

Look at the clip again, make sure you're not messing it up.

Spray again LIGHTLY.

You don't want to build up a thick goop on the outside or it will be awful looking and you'll ruin your thing.

Let it dry.

Don't handle it while it's drying.

Did I mention to spray LIGHTLY? (It will make all the difference).

Could always use clear nail polish

How does it clip?

It it's simple, and you want, take a picture with a zoom lens from a decent distance away, straight on, with no angle at all. Then measure the height, width at widest point, and thickness.

If I have time after the holiday, I could craft that into a 3D model that you could provide to a place like PCBWay to have printed, or even machined in actual brass.

Posting that in a 3D Printing or CAD community might also find you a volunteer that could do this for you with a more definitive timeframe.

That being said, thats easy with a flat piece, but I'm not sure what I'm looking at as a "clip".

A clearcoat spray paint could work.

Do check what the optimal humidity conditions are first, since it can turn cloudy if it is too humid and that is very noticible on small objects.

Maybe a couple of coats of slightly thinned clear nail polish?

Just two cents here - not an expert. Brass that is unlaquered oxidizes and tarnishes extremely easily, and touching it with your skin/hands will certainly do that. If it used to stay shiny, the laquer or other coating probably has worn off. No biggie.

Get some brass polish from a hardware store and clean it up. You may want to hit it with some very fine steel wool first to clean off any remaining laquer/coat for an even polish. If you want to keep some parts darker, be careful and finicky to only polish what you want to brighten up.

Fresh clear coat or a laquer when you're done would keep it looking shiny when done. Make sure all of the polishing compound has been completely wiped clean before you coat. Wear gloves when you polish to keep skin oils and salt off the material.

If you clear coat it as is, it will just be maintain the current tarnish, which doesn't sound like your goal.

Personally I like how brass weathers and patinas. Google brass finishing to find guidance from the internet freaks.

Similar to the nail polish suggestion, they also make clear spray paint.

dip it in lacquer or epoxy, shave out the middle where the paper goes once it's set?

Can I ask where to buy one

I don't know how much you want to spend or how many other things you might want to preserve. But they actually make specific lacquers for jewelry.

https://www.riogrande.com/product/midas-clear-lacquer-sealant-and-tarnish-inhibitor/335149GP/?code=335149

You can also find them on Amazon.

https://www.riogrande.com/product/midas-clear-lacquer-sealant-and-tarnish-inhibitor/335149GP/?code=335149

I bought the one on Amazon, it was absurdly expensive for what it is, but I wanted to protect a slice of meteorite from rusting.

I seriously think No.

This is a mixed-material piece that looks good but is going to be destroyed regardless. Modgepodge, lacquer, shellac, varnish, clearcoat... they're all going to wreck it. There are too many "metal coatings", films, paints and so forth on this. Just use it and throw it away, looks like it's cheap Chinesium

There are brass paints you could apply and then seal it with any of a variety of products. I use something called Protectaclear, but you could get a cyanoacrylate spray, or something like that. Don’t get something cheap and generic because who knows what crap they might put in there.