Where can I get a new battery for my iPhone X?

No, you will need to take it to an Apple store for repair, or send it in for repair. Do not use a 3rd party repair shop, it won't be a genuine replacement part and you will run into problems.

iPhone Battery Replacement.

iPhone Battery Repair & Replacement - Apple Support

No. You can have the battery replaced at an Apple Store or authorized service provider.

If there is no Apple Store near you, most Best Buy stores are authorized Apple service providers.

Here is how to get your battery replaced, if it needs replacing→iPhone Battery Replacement - Official Apple Support. Apple will first run a diagnostic to see if it needs replacing.