Which drivers are supported largely depends on the node OS (COS or Ubuntu) and the GKE version the node is running. When you add a GPU node to your cluster, GKE provisions a DaemonSet that automatically installs the drivers for you. A list of supported NVIDIA driver versions per GKE version can be found in the document [1] that Google has at present.
The Nvidia drivers on your cluster get updated when the node itself gets an update to the newer version of GKE. You can follow the newest feature release of GKE in the document [2].
Now, as we do not have the required NVENC driver version, an alternative approach might be to pull required older version of FFmpeg.
[1]--https://cloud.google.com/kubernetes-engine/docs/how-to/gpus#installing_drivers
[2]--https://cloud.google.com/kubernetes-engine/docs/release-notes