Can I transfer my photos to an external hard drive to free up space on my Mac?

If you mean the Photos.photoslibrary, you can move the entire Library to an external drive, then tell Photos to look there for the Library.

Once moved, hold down the Option key and open Photos. It should ask which Library to open. Choose the new copy on the external.

Once opened and all looks good, go to Preferences and set that library as the System Photos Library. It should show the path to the library on your external drive.

Make sure the checkbox to copy items into the Library when importing is set.

If everything looks good (maybe close and reopen Photos and make sure it is selecting the external drive library in Preferences), all photos appear to have been transferred, you can delete the Library on your internal drive.

Don't forget to backup the external drive. Time Machine will backup external Mac-formatted disks, but you need to check that it is not excluded in the Time Machine System Preferences.

Sigurd56 wrote:

How can I transfer my photos to an external hard drive? I need to free up space on my Mac

This implies removing from the present location. ?

Or does one mean exporting to External Drive and then removing them from the Internal Drive.

If iCloud Photos is in play - suggest signing out of iCloud before attempting.

Doing otherwise will remove the photos from All Other devices syncing to iCloud - Photos once they are transferred off the Internal Drive.