Hi Clamp58,
welcome to this Apple (user-to-user) Community!
Re: Music Library: "If I move the library to exist on an external drive, does the entire library move to the hard drive or only new (imported) files from that point on?"
Seldom, if ever, do I use the Music app to play files of the music I enjoy.
If that is what you intend, I may not be the best person to inform you.
At least, we get your discussion under way, and provide opportunities for others to share their expertise.
Music files on my Mac are always accessible as files in folders. .
You too, may have the control over how you use the external hard-drive and store and play your Music.
Generally an external hard-drive would store back-up copies of any, or all music files stored on your Mac.
You can add more files whenever you wish.
If you intend to use "Time Machine" and the external hard-drive has plenty of space you can back-up all files on your Mac, and have access to any of them. You can choose how often you want to add files to the back-up, or it can be set to remain connected and back-up everything on your Mac continuously / automatically / or at intervals.
If not used with Time Machine: An external hard-drive can be used just for Music in other ways.
Eg: You can just "drag" any files (or folders) that you want to the hard drive, or copy the whole Music library.
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Re: "Move my Music Library to an external drive?
I would like to free up the storage space taken up by my Music library on my hard drive."
As your goal is to recover the storage space on your Mac, you are the one to decide whether all or some of the music is deleted on the Mac, after storing all or some copies of your music files on the eternal hard drive.
Please be aware you will not have any back-up of your Music if the Music files exist only on the external hard-drive. Many of us prefer to have at least two, preferably three copies of any treasured or difficult-to-replace files safely stored. That way if a hard-drive, or a particular file, gets somehow lost, stolen, inaccessible, or damaged, it's not such a loss.
All the best :-)