Hi
The best way is to sync iCloud with a new empty library:
1 - Make sure your external drive is formatted correctly as described here:
2- Prepare it as described at the link below:
It must be formatted APFS or MacOS extended (journaled), and not be (or have been) used for time machine. It must have the 'ignore ownership" checkbox ticked. It should not be on a memory stick, SD or similar. It stands to reason that if you want any sort of reasonable performance it should be a fast drive with a fast connection.
See
Move your Photos library to save space on your Mac – Apple Support (UK)
3 - Create a new EMPTY library on the external disk. (Hold down the option key while starting photos and click "create new")
4 - Open the new empty library in photos.
5 - In photos preferences set it to the system library (click the button)
6 - In photos preferences iClound - turn icloud on with download originals.
7 - Wait - for photos to download all your images from iCloud into your freshly minted library. It may take some time - possibly days. Leave the mac on with photos open while it is doing it.