The very first thing to do when purchasing an external hard disk drive is to erase it using Disk Utility. Disk Utility is in your Mac's Utilities folder.
Select the drive, then the Erase button. Make it look like this:

The Name is up to you but the other options should be as shown. Click the Erase button to erase the drive.
Then, in the Mac's Photos app, select the photos you wish to archive, then use its File > Export... function. I suggest you select the "Export Unmodified Original..." option unless you prefer to save an edited version. Designate the external drive for the destination.
Then, you can erase those photos from your Photo Library. Use the Image menu > Delete, or press the Delete key on your keyboard.
You're almost finished. Deleted photos will be placed in an album named Recently Deleted. It has a "trash can" icon. They will remain there for the period of time shown, after which they will be permanently deleted. To delete them right away, click the Delete All button, then confirm the dialog that appears next.
Finally, consider creating a backup of your exported photos. To learn how to use Time Machine read Use Time Machine to back up or restore your Mac.