Microsoft today released a new update for Skype Insiders on Android devices. This v188.8.131.52 update brings support for Android tablets. Skype team has mentioned that this version of Skype is specifically built for Android tablets of all screen sizes. This update also comes with a known issue, you can´t answer calls through lock screen. If you can live with that, download it from Play Store and give it a try.
You can download the Skype Insider Preview build here.