Apple Music and iCloud Music Library sometimes face slight delays when syncing your music between devices like a Mac and iPhone, but since the launch of iOS 11.3 reports about these delays have grown much more frequent. On the MacRumors forums, in Apple's support communities, and throughout numerous Reddit posts, users have mentioned that when they add new music on their Mac or iPad, it no longer appears on their iPhone.
Some users have said that toggling iCloud Music Library on/off works to kickstart the sync and force a refresh of albums on their iPhone, but that has the potential to cause further problems like deleted music and the removal of some song downloads. Fortunately, one user on the Apple support communities website has shared a helpful temporary fix for the issue, which MacRumors has been able to successfully perform more than five times.
To manually refresh your iPhone's music library, simply create a new, blank playlist by navigating to the Library tab in the iOS Music app, tap Playlists, tap New Playlist, and tap Done. Once the refresh is done, jump to the bottom of the Playlists page and 3D Touch to delete the empty playlist. Note that this will also update songs added and removed within playlists.
There is no fix for this, but there is a work around until Apple fixes this: just create a blank playlist on the iOS device. This forces a read/write with the library stored in iCloud, then all your changes will suddenly get pulled down. You have to do this every time, it's essentially a manual refresh now.
Unfortunately, the reverse method doesn't appear to work as consistently in iTunes on Mac, but desktop users also have another potential easy solution to refresh their library: simply rate a song by loving/disliking it. Afterwards, the Recently Added tab in iTunes should refresh with the addition or removal of content that you made on any other devices connected to the same iCloud account.
On both macOS and iOS, you can also add any other new song, album, or playlist to your library to manually refresh and force the content not syncing across devices to appear. Then, you can delete the new songs after everything else has been updated.
Multiple Apple Music subscribers have opened up support cases on the bug, and Apple support in most instances have said that it's not a known issue. However, support staff told one user that they will start an investigation after he "rebooted, changed password, signed out of iCloud, switched iCloud music library off," and more.