We are currently using FME server version FME Server 2021.1.3 and FME Workbench 2021.0.1 and we wanted to upgrade the FME server to the latest version, so if we upgrade the server will it be some issues with the old workbench automations already running in the FME Server. Or the old workbench is compatibile for the upgraded FME server ?
Old workspaces are compatible with a new FME Server (FME Flow nowadays) but they might benefit from updating transformers, readers and writers.
If you open an old workspace in a new version of FME Workbench you'll see a category of "Upgradeable Transformers" in your navigator, go through them to update them to the latest versions. You don't have to do that, but depending on the actual transformers you're using it might mean a very significant performance boost.
I would definitely recommend testing your workspaces in the new version to make sure they run as you expect. While FME is backwards compatible there can be cases where things do break unexpectedly.