As promised, Google is now releasing their monthly Nexus security updates. After the Stagefright exploit was discovered and patched, the Mountain View-based giant has announced that security updates will be released for their Nexus devices each month.
T-Mobile revealed on their support website that a new software update is now being pushed to the Nexus 9 LTE and Nexus 7 2013 LTE owners. The new firmware is based on Android 5.1.1 and it arrives with build number LMY48M. It appears that the new software arrives with "Android security enhancements" and "minor bug fixes", so don't get your hopes to high.
The new Android 5.1.1 Lollipop update for T-Mobile Nexus 7 and Nexus 9 has a size of around 20 MB and, as usual, the roll out is made in phases. This means that it will take several days until the new firmware spreads to everybody. Just like it happens to other over-the-air software updates, you should be notified as soon as the update becomes available for your tablet. Just tap on the system update message, choose 'Download now', wait until the download completes, then select 'Install now'. Your device should reboot and flash the new firmware. In case the system update notification failed to appear, you would want to check for the update manually under Settings > About device > System updates > Check now.
It's also worth adding that only the Nexus 7 2013 and Nexus 9 devices that run an official Android build will receive the new update. If you run a custom ROM or you altered the software in any way, you must wait until the factory image files are released in order to be able to install the new version.