The original Live:Air was introduced in March of 2015, and was removed from the store for new purchases in September of 2017, shortly after the release of Live:Air Action.
Although the original Live:Air is no longer available for purchase by new customers, it's possible for customers who previously downloaded the app to download it again by checking the purchase history in the app store account; make sure that you're signed in with the same Apple ID that was used to make the original download and any in-app purchases.
Customers can continue to use the Live:Air app on your iPad, but all development effort is focused on the newer Live:Air Action app.
Shortly after Live:Air Action was introduced, Teradek had an interactive stream highlighting the features of the new app:
The Live:Air Action app is based on a new architecture that was written from the ground up to support more live sources and graphic layers, and to allow newer features (e.g. HEVC/H.265 support) which would not have been possible in the original Live:Air app.
Purchases from Live:Air don't transfer over to Live:Air Action. While we can understand that customers who had purchased Live:Air would be very happy to receive Live:Air Action at no charge, this was a decision by the product management team to allow continued development on the app, and to help support development on our free Live:Air Solo and Live:Air Remote apps.
The overall cost for Live:Air Action is less than the original Live:Air add-ons, and there are more granular controls over features so that you can purchase just the components that you need at a lower cost.
Additionally, if you purchase the Live:Air Action Bundle you receive not only the current in-app purchases at a fixed price, but all future in-app purchases at no additional charge, as described in this article:
Since the Live:Air Action -- without any purchases -- allows some of the same functionality that was only possible with paid purchases in the original Live:Air (no watermark on stream, streaming longer than 30 minutes, etc.), we encourage customers to download and try out Live:Air Action for free.