In the past, I have had issues where Exchange 2013/2016 will not take the license key in the Exchange Control Panel.
Luckily it’s easy to do it with Exchange powershell, do the following:
Run Exchange Powershell as Administrator,
Run the following command, replace ServerName with your server and your insert your key.
Set-ExchangeServer ServerName -ProductKey
Key is generally 25 Characters, (XXXXX-XXXXX-XXXXX-XXXXX-XXXXX)
Once the command has completed, restart the Microsoft Exchange information store service and your license for your Exchange 2013/2016 will be active.