Sync iTunes library with edited app list

It isn't exactly clear what you're asking for here. iTunes Match provides a library syncing service for the music section of your library. If we assume that all of your music is either matched or uploaded then if you were to hold down shift as you launch iTunes then use the create library option in the dialog that appears you could create a new library on your external drive in a suitable location. As long as Sync Library AKA iCloud Music Library is enabled this library will show all of the music that has been added to your account, all being in the cloud. Is this what you are after? Or are you currently using a library that isn't connected to your iTunes Match account? Or did you perhaps clean up duplicate entries in the library leaving behind redundant files in your media folder that you're now looking to eliminate somehow?

Please note that iTunes Match is not a backup service. You should maintain at least one version of your library where all content is downloaded to that computer and ideally backed up to an external hard drive for security.

tt2