Conflict with iCloud Size and HardDrive limitations

It's hard to tell exactly what you're asking.

• Are you wanting to transfer pictures from iCloud.com to an external drive?

In Safari (for instance) Settings>General set the Downloads location to the external drive. You'll have to decide if you want the Unmodified Originals or the edited version of the pictures. If you want both, it will take twice the space.

• Do you want to use Photos with your Library located on an external drive?

Then first be sure the drive is formatted in either APFS format or Mac OS Extended (Journaled) format. Then you can create a new empty Library on the external drive (close Photos, option click the Photos icon, and choose Create New from the Library dialog,) set the new Library as your System Library (Photos' Settings>General) and sit back and wait for it to fill from iCloud. I will take awhile, but it will take up only half the space of downloading individual pictures, and there will be much more information.

• If you just want to move your existing Photos Library to a properly formatted external drive, see this:

Move your Photos library to save space on your Mac - Apple Support

Let us know what you want, and we can give more explicit help if necessary…