Your compendium is attached to either the world or a module. If it’s a module, you can simply upload the module through the Import Wizard and that’s about it.
Some caveats come into play when dealing with for example VTTA’s shared module, as it’s an official module, The Forge may see it as a duplicate and not even import yours. For that you would need to edit the module.json in the module directory and change the name and version to something unique to you (to not be confused with an existing module).
If your compendium is attached to your world and you would like it to be separated, you would need to create a shared compendium in the forge, export it (from Export Game Data on the My Foundry page), and replace the packs/spells.db with your own compendium file from your world. It should work if your entities are all Items, which they probably would be anyway.
Then you can delete the shared compendium from The Forge and import your changed one through the Importer Wizard.
Hopefully you’ve created a new module from the get go and will be able to just import it on The Forge and everything works, but if not, I’ve outlined the most likely paths you’d need to take.
Let us know how it goes.