From the README
In order to update kasm, first make sure you are using the latest docker image, and then perform the in app update in the admin panel. Docker image update and recreation of container alone won’t update kasm.
I wasn’t able to find the update/upgrade option in the admin panel after pulling the latest image, however I was able to perform the update by entering the kasm container (docker exec -it kasm bash) and running (bash /kasm_release/upgrade.sh)