How do I import an iTunes library from external drive to Apple Music in Catalina?

You can press and hold down option as you launch Music to access and convert an existing iTunes library to Music. You can choose where to save the converted library, so you could store that on the external drive too.

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See Move your iTunes library to a new computer - Apple Community for more on moving the library from one computer to another. If you have either iTunes Match or Apple Music then whatever you have locally should be merged with what is already in the cloud when you enable Sync Library (aka iCloud Music Library).

If you've somehow deleted your content in the cloud then locally stored tracks might be marked as removed from the cloud when the library syncs, but they shouldn't actually be deleted, and they can be added back to the cloud library.

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