vSphere Kubernetes Service 3.x
An embedded version of the supervisor service, also known as Tanzu Kubernetes Grid Service is coupled with as well as managed by the vCenter Server. In case the vCenter server is upgraded/patched to a version higher, the Tanzu Kubernetes Grid Service can only be upgraded to the version which is coupled with that version/build of vCenter Server.
For example- vCenter Server 8.0u3g comes with TKG service version 3.3.3. Therefore, an upgrade of the TKG service from 3.3.1 to version 3.3.3 directly can be performed successfully. To be able to upgrade the TKG service version from 3.3.1 to 3.3.2, the vCenter Server needs to be on version 8.o u3e.
Use the Asynchronous version of the Tanzu Kubernetes Grid service instead which can be obtained/downloaded from the Broadcom Support portal. This Asynchronous version package is called as "Kubernetes service". This way you don't have to rely on the "Tanzu Kubernetes Grid" service version which comes embedded, and you get to choose and customize which Kubernetes service version you'd like to be on.
Refer the following documentation on installing a Supervisor Services, including installing a version manually- GitHub - vsphere-tmm/Supervisor-Services: Supervisor Services