Hey there! To add to @tygb’s post, you can easily drag and drop the library onto your external HD.
Likewise, if ALL the photos that you need are already in iCloud, you can simply create a NEW Photos Library on your external drive, and download all your photos directly to it:
Create additional photo libraries in Photos on Mac:
https://support.apple.com/guide/photos/create-additional-libraries-pht6d60b524/mac
Just Quit/Launch Photos holding the Option key, choose “New Library” and change the location to your external HD.
Once done, you just have to change this library to the default library, as iCloud will sync with only one library at a time:
Designate a System Photo Library in Photos:
https://support.apple.com/en-us/HT204414
Once the new, empty library is opened, just click, (On the top menu): Photos > Preferences > General, and click the option to “Use As System Photos Library”.
Next, click on the “iCloud” tab, and enable iCloud Photos, before you know it, all you photos in iCloud will download directly to your external HD. And, if you leave it plugged in, any photos you take on your other devices that also have iCloud Photos enabled, will automatically be downloaded to the photos on your external HD!
If you’re trying to save space on yo Mac, as said before, you can simply move the Photos Library to the trash and empty it once all are downloaded to the External HD.
I like these options as well, because you can buy external storage for fairly cheap, and makes it easy to store your Photos and even Music to the external HD, AND Make it the default Photos or Music Library, which, as long as connected, you won’t notice a difference when launching it using the apps!
Likewise, if you do want a physically copy of the Photos on the external HD, make sure in the Photos Preferences to choose, “Download and keep originals”, once all there, you could simply, if you wanted, disable iCloud Photos, and keep that library as a backup, or keep it as the default library and import your iPhone, etc., photos directly to the external Photos Library using a cable, etc.
You can also, as the article states, switch between different Photos Libraries by launching the Photos app while holding the Option key.
And with that feature, you can even make one library that DOESN’T sync with iCloud at all, and still use another library that DOES!
Note, that when you initially disable iCloud Photos, if the Optimize Storage option is turned on, (Used to save space on your Mac), you will get a prompt telling you that, “This many high resolution photos will be deleted from your Mac”, you can choose the option to delete. Don’t worry, the photos are still in iCloud, available to download to your external drive, or anywhere else that has sufficient storage.
Hope that helps!