HOW TO Move a media library
Choose a drive
Find an external drive that has enough free space on it to house your Music library. Remember to leave room for songs you download or rip in future. Connect it to your Mac. It’s best to keep it permanently connected.
Copy your Library
Navigate to your user folder and go to Music > Music. Grab that second Music folder and drag it to the external drive. Wait for it to copy across. Once it’s finished, check it has copied everything. Consider making a backup copy.
Point at the new library
Launch Music and go to Music > Prefs. Click on the Files tab. Click Change and go to the folder that now houses music. Click Open. Quit Music. Now delete the original Music folder and restart Music.