Skype 6.3 has now been released and it includes support for iPads and iPhones running on iOS 9 as well. It also brings around various new features such as split view and slide over.
The new Split View and Slide Over features make it possible for the user to use another app alongside Skype. You can easily share links and do other stuff without disrupting your Skype call or chat with your friends or relatives.
There is a new feature that allows you to reply to chats in Skype without having to open the application. You can directly reply to a notification from your lockscreen. Make sure you have your Skype notifications on (go to: Settings > Notifications > Skype > Allow Notifications. Then choose whether you want Banners) to try this out.
There is also the open to start a Skype chat from spotlight. For example, if you search for a contact in spotlight, you can just tap on the shortcut to open a chat on Skype.