Hi MRF.
When upgrading your storage system from Data ONTAP 8.1.1 to Data ONTAP 8.2, no new license keys are needed unless your system is clean. However, you should be aware that any HA failover pairs you have also need to be upgraded and licensed, or else when a failover occurs, the system will detect a non-licensed controller and give you a 90 day grace period in which you can license your failover controller.
You should also be aware that Data ONTAP 8.2 license keys are longer than 8.1.1 keys. The NetApp Support Article for licenses when upgrading to Data ONTAP 8.2 can be found here: https://kb.netapp.com/support/index?page=content&id=3013749&actp=RSS
I hope this message has been helpful,
Nicolaikay