How did you transfer the Information to the new iPad?
Did you restore a backup from the iPad 2 onto the new iPad Air? Did you use the same Apple ID on the new iPad as you were using on the old one?
If you did restore a backup from the iPad 2 and are using the same Apple ID, then available apps should have been automatically downloaded to the new iPad from the App Store. The missing Apps may no longer be available on the App Store and/or are likely to be 32 bit apps, and as such incompatible with the new iPad's operating system.
You can open the App Store, tap on the icon at the top right corner, and then on Purchased and see what apps are still available and compatible with your new iPad from your purchased list.