Today, Microsoft announced that it's upgrading everyone on Skype classic version 7 to version 8. Version 8 came out of beta last October, but it was only available on Windows 10 1511 or earlier, Windows 8.1, or Windows 7. If you were on version 1607 or later, Microsoft wanted you to use the UWP app.
Moreover, anything older than Skype version 8 will stop working on September 1, so you're going to want to upgrade your client. It's a bit of a surprise move, as many expected that after Microsoft killed version 7, it would leave the UWP app as the only way to access the service.
Indeed, the entire time that Skype version 8 was in beta, and after that, there was no way to install it on newer versions of Windows 10 without some workarounds.
Skype version 8 is designed more similarly to the UWP app, as well as the mobile apps for iOS and Android. Here are the features that Microsoft outlined in Skype version 8:
Free HD video and screensharing calls—Get together with 1 or 24 of your friends, families, or colleagues no matter what device they use Skype on. See everyone in high definition, view 1080px video, and share things together.
More productive messaging—Express how you’re feeling by reacting to messages in conversations. Use @mentions to easily grab someone’s attention in a group chat. Simply type the @ symbol followed by their name to trigger a notification for them. You can easily find all your @mentions and get back to people in the notification center.
Chat media gallery—Looking for the link or photo sent a few weeks ago? Chat media gallery makes it easy to find files, links, and photos that were shared in a conversation, whether it was yesterday or last month. No more scrolling through your chat history—just click Gallery under the chat name to see all the files, links, and photos in the conversation.
Share photos, videos, and other files—Share up to 300 MB at a time over Skype just by dragging and dropping files into your conversation window.
The specific version number of the new app is 18.104.22.168. You can upgrade by going to Help -> Check for updates in Skype version 7. Or, of course, you can wait until Skype upgrades you automatically. If you want to check out the desktop variant of Skype, go here and choose 'Skype for Windows'.