Trying to transfer Music not purchased through iTunes ITUNES

Assuming those pieces of music is already imported to iTunes on an Apple computer, the easiest (but not the cheapest) way is probably to subscribe to Apple Music (more expensive) or iTunes Match (cheaper) and authorize the new iPhone or computer for Apple Music / iTunes Match. Here is a discussion and comparison of both services. You may also need a good mobile data subscription plan if you can not store all of your music on your iPhone when your music library is large.

If you don't want to subscribe to the either service, you can manually sync your music library on your computer with that of iPhone using the Finder (macOS Catalina) or the iTunes (macOS Mojave or earlier).

(Below is an expanded version of my earlier post. Sorry I had to repost because I can not edit or delete my first post.)

Assuming those pieces of music are already imported to the Music app or iTunes on a Mac or a Windows PC, the easiest (but not the cheapest) way is probably to subscribe to Apple Music (more expensive) or iTunes Match (cheaper) and authorize the new iPhone or computer for Apple Music / iTunes Match. Here is a discussion and comparison of both services if you don't have either of them at this time. You may also need a good mobile data subscription plan if you can not store all of your music on your iPhone when your music library is large. 

If you don't have or don't want to subscribe to the either service, you can manually sync your music library on your computer with that of iPhone using the Finder (macOS Catalina) or the iTunes (macOS Mojave or earlier). 

To move your music to a new computer without subscribing to the either service, you need to locate the existing music files on your computer (they are likely to be somewhere under /Users/{your username}/Music/ directory) and copy them to a USB drive. You can then import these from the USB drive to your new computer using the Finder or the Music app (macOS Catalina) or the iTunes (macOS Mojave or earlier).

Hope these help.

I assume you have transferred your music (files) to another computer using the directions I gave in the last paragraph. You should be able to transfer all your playlists using the instructions below but I don't how you can transfer other metadata.

1) Export a copy of all your playlists via File > Library > Export Library in the Music or iTunes app on your computer, for example onto a USB drive, choosing XML from the Format / Save As pop-up menu,

2) Import those playlists on the other computer using File > Library > Import Playlist in the Music app on your other computer choosing the file in XML format on the USB drive.

Here is the Apple Support page with these instructions.

Hi, I followed these instructions, but found that my metadata (play counts, playlists) were not imported. any advice?

many thanks