Hi Jason,
The latest version of Airwave available is the 7.7.1 version.
I would recommend you to first upgrade to the 7.6.x version and then move to the latest 7.7.1 version.
Also, the 7.7.1 version needs the Cent OS version 6.2 for it to work. I have attached a document on how to migrate to the 6.2 Cent OS version.
To check Cent OS version:
# crr
If the cent OS is below 6.2, please follow the steps in 6.2 migration document.
If Cent OS version is 6.2, then you can do a upgrade to 7.6.x and then upgrade to the latest 7.7.1 version.
Another important thing to keep in mind is your Hardware. I have also attached the hardware Sizing guide for the 7.7 version. please go through and make sure the server has enough resource to run the latest version.
Also, please take the backup of the server and save it locally before any upgrade. Steps are in the Cent OS migration document.
Please let me know if you need more clarifications.