Make sure you have Sync checked for the Google Music app:
* Go to Settings > Accounts > Google.
* Then under Accounts, tap the account name that you use (if you only have one account, that will be the only one available).
* A new menu will appear. Scroll down to Google Play Music and make sure the box is checked, which allows for sync.
Other things to try:
* Go to the Settings menu in the Google Music app, and tap the "Refresh" option.
* In the upper left corner of the app, make sure that you have it set to "All Music" in the drop down menu, not "On Device Only".
* Make sure you are connected with the correct Google account (in the Google Music app settings).
* Clear the cache (from the Nexus 7 settings menu).
* Reboot the N7.