Sticky faucet handle of unrecognized faucet
It looks much like this one--wow ... not cheap--found by doing a web image search for "antique brass faucet".

This is the install document. Item 16 is a setscrew that you loosen so that you can remove the handle, and expose the cartridge assembly. Then I guess that you would loosen a retaining ring and pull up on the cartridge assembly.

Do not forget to shut off the water before doing this.

Here is the manufacturer. You could email them.

Here is a search for info.