This article explains two methods for syncing some of your iTunes songs to your iOS device. These instructions apply to iTunes 12 and later. However, if you're an Apple Music member or have an iTunes Match subscription, iCloud Music Library is enabled and you won't be able to manually manage music.
How to Fix Apple Music Library Not Syncing Issue
If you have a large music library or an iPhone, iPad, or iPod touch with limited storage, you may not want to sync every song in your iTunes library to your iOS mobile device. If you store and use content other than music, such as apps, videos, and e-books, you may want to customize how you sync. To manually manage music and transfer only certain songs to your device, turn off songs in your iTunes library or use the iTunes Sync screen.
To sync only selected songs in your iTunes library to your computer, you'll first need to change a setting:
Open iTunes on your computer and connect your iOS device.