Since this is a terminal server I would recommend installing the client in Shared deployment mode. What this does is it installs the client to a common/public user profile. Then any additional users that login would use the binaries from the common/public user profile and only information such as last used project would be stored in the user profile. The initial installation should preformed as an Administrator and IE should be started with ''Run As Administrator''. After that you should not get prompted for administrator creditials when starting the client.
Here are some links to documentation on Shared Deployment mode on the HPE Knowledge Base Site
Understanding the different deployment modes in ALM 11.x and above
How does the ALM 11 Shared Deployment differ from a standard deployment