Preserve large oakbrush branch with leaves?

I'm not sure about preserving the leaves, but you can probably use a spray sealer on the branches after the dry out. Here's a link on preserving the nest:

https://sciencing.com/preserve-paper-hornets-nest-8183289.html

For the nest:

But rather than control the hornets and risk ruining the nest, why not take it down and hang it up for display. I can attest; they are great conversation starters.

The easiest method of collecting a nest is to wait until after the hornets have abandoned the nest in the fall (after the first hard freeze or by late October). Collect the nest as soon as possible because exposed, unprotected nests are subject to destruction by wildlife and weather. There may be few, if any hornets in a nest collected in late fall. If you feel the need to be extra-cautious, leave the nest in a garage or porch where it will be protected from the weather until mid-winter. Then bring the nest indoors for display. Leaving the nest in the garage also eliminates the slight risk that the carcasses of hornets and larvae that remain in a collected nest may produce a mild odor before they completely dry up.

It is not necessary to treat the collected nest in any way. Varnish or preservative is not required. The nest will last almost indefinitely if it is suspended in a dry location where it will not be damaged by handling or vibration. Just hang it up, sit back, admire and enjoy!

ref:https://www.extension.iastate.edu/news/2006/oct/070901.htm

For the leaves, you could get any can of ordinary hairspray and spray them, preferably outside, shake the can for about 20 secconds before use. This will not guarantee them from dropping, only preserving them.

For the oak branch:

Wipe down the entire branch with a dry paper towel to remove all the dust and debris. Use a chip brush to apply a generous coat of stain. No need to wipe off the excess stain, leave it to soak into the wood for 24 hours. Finish the branch with 2 coats of polyurethane in satin to protect it and you're done!

I agree with Ann's reply I think a spray on sealer would probably do you good on the whole thing!

The safest way to collect the nest is to wait until after a few hard frosts, but then get it before weather conditions destroy it. For an extra margin of safety, the nest might first be moved into a protected spot such as a garage or porch until the middle of winter.The only hornets left in the nest by that time would be in the form of eggs laid by the old queen. If any of them were to hatch, the resulting grubs would die quickly because there are no workers to feed them.

As far as preserving the leaves this should help:

https://ourpastimes.com/how-to-preserve-fall-leaves-branches-for-centerpieces-for-free-12001180.html

Spray with clear drying sealer after drying and preserving. A friend of my husband once thought he had a dormant/empty hornet's nest and brought it inside. When the heat warmed it up, they had a swarm. So you want to make sure that is taken care of before bringing into your living area.

you need to be sure hornets are out of the nest before bringing inside -

If it were my project I would consider using some artificial silk leaves of the very same nature and replacing them as you see now. The circle leaves could be even hand colored the precise hues that you favor. Attempting to keep the natural leaves the same color and not brittle could be quite a challenge.

I would wait until the hornets nest leave

Go to Michael’s craft get spray varnish and spray it all over like one coat. Let it dry out good all the bugs will leave because of the smell and then hou could realy spray it good to save it.

Thank you all for your ideas! If I remember a year from now I'll let you know how it's holding up!

i would spray it with chemical and let all leave and then preserve to use at home