Storing photos on external hard drive

See instructions in: Move your Photos library to save space on your Mac - Apple Support

Drag and drop the library to the external to create a copy. Do not just move it. Test the copy thoroughly, before you delete it from the system volume. And remember that you now have to include the external volume into your Time Machine backups, so you will still get backups of your photos.

And pay particular attention to the format of the drive (APFS or MacOS extended, journalled) and not storing on any ethernet or wifi connected drive)