If you're adventurous and use Nokia Care Suite or Navifirm+, you can download the ROM and manually flash your device (losing all information in the process); alternatively, you can wait until your carrier begins to roll it out over-the-air, which is what we recommend.
Manually flashing a Lumia 720 with Amber update
Nokia’s Amber update for the Lumia 720 (and the 620 and 520) have been slower to be released when compared to the high-end Lumias, though Nokia has promised that all devices should be updated by the end of September. Lots of people have been looking forward to the Lumia 720 update as that device is quite popular. With the new files on Nokia’s servers, it means the OS build is finalized and it should be rolling out to the various regions within the next few days.
New Glance screen on the Nokia Lumia 720 + Amber
Windows Phone Central can confirm that Amber on the Lumia 720 brings with it Data Sense, Glance Screen, FM Radio, default-camera selection, Lumia Color Profile, Call + SMS filter and the Other Storage fix, amongst the top items. Although double-tap to awake is supposed to be there, we have not been able to find that feature enabled for the Lumia 720 on our device.
We’ll keep you posted when the update starts rolling out over-the-air. In the meantime, head into our Lumia 720 forums for further discussion: http://forums.windowscentral.com/nokia-lumia-720/
Thanks, husam2277, for the tip