I need to update a cluster of two Riverbed Traffic Managers from version 9.8r2 to version 20.3. I was told that I need to create new virtual appliances to do this update, updating one appliance at a time, loading a backup from the old LBs into the new LBs, and using the same network parameters as the old ones. However, I am not sure how I will apply the licenses from the old appliances to the new ones, should I download the license files from the support site and load them in the new appliances? Will those licenses work for the new version? Is there any additional work I should do for this update?
Yes you'll need to do a new install, per condition 4 on https://kb.pulsesecure.net/articles/Pulse_Secure_Article/KB44475, which links to https://community.pulsesecure.net/t5/Pulse-Secure-vADC/Upgrading-and-reinstalling-Traffic-Manager-Vi... for how to do it.
Also please upgrade to the latest 21.1 now, not 20.3, because of https://kb.pulsesecure.net/articles/Pulse_Security_Advisories/SA44790
If the IP addresses stay the same then you can use the same licenses, which are in the backup file, otherwise you can raise a support case to have the licenses re-hosted to a new IP.
Note that there's a known issue with importing backups from versions before 17.2, which is that the network interfaces have changed names. To make the import work smoothly you can manually extract the backup tar and edit the files conf/zxtms/hostnames, change the interface names to match the new machines, then re-tar up the backup file. (Upgrading in place works because the upgrade process can see the rename happen, but importing the backup can't tell what the mapping from the old names to the current names is).
If you need further assistance with this and if you have an active support contract then please open a support case.