We have an application (Product) that, when it's deployed in UAT for any User/Client, a completely new server (Infrastructure) / Domain is set up along with the database, but the code base is the same as for the earlier User/Client.
If we run a regression suite for User/Client A, then do we also need to run the regression suite again when User/Client B is onboarded?
You should perform a risk assessment to decide if it's necessary. If the environment - the hardware, the versions of all dependencies, the configuration of all tools - is identical, then you may find that the risk is low and regression testing is not necessary. However, if you determine that the hardware is different (perhaps due to obsolescence) or a dependency has changed (perhaps due to security patching or new versions being released and old versions being end-of-life), you may want to assess what has changed and think more carefully about if and what to test.
I would suggest at least a smoke test to verify that the system, all its dependencies, and all configurations are correct. A smoke test would be a small subset of the whole set of regression tests selected based on their ability to confirm the installation and configuration of key components of the system before handing it over for end users to perform UAT activities.
It depends on how different and separate the setups are.
You may want to regress areas that are dependent on client configurations. After all, you don't want to Acme Amalgamated see branding for Great Group, or vice versa.
If they share common components, like a single database, you may want to regress more deeply to make sure that user permissions don't leak over, or other security issues.
If there's absolutely nothing in common, you may be able to get away with just checking that all the appropriate pieces of each system are talking to their own system and not something else.
Generally you don't need a full regression if you aren't changing code. You definitely want to make sure your configurations are correct and that the systems are truly separate.
