How to run one container and finish a job, before another container starts using kubernetes?

Use initContainers - updated your deployment.yml, assuming example.com/nltk_data:latest is your data image

How to write to a shared volume without having that shared volume overwrite?

As you know what is there in your image, you need to select an appropriate mount path. I would use /mnt/nltk_data

Updated deployment.yml with init containers

spec:  volumes:    - name: shared-data      emptyDir: {}  initContainers:    - name: init-ikg-api-demo      imagePullPolicy: Always      # You can use command, if you don't want to change the ENTRYPOINT      command: ['sh', '-c', 'cp -r /nltk_data_source /mnt/nltk_data']      volumeMounts:        - name: shared-data          mountPath: /mnt/nltk_data      image: example.com/nltk_data:latest  containers:    - name: ikg-api-demo      imagePullPolicy: Always      volumeMounts:        - name: shared-data          mountPath: /nltk_data      image: example.com/main_api:private_key      ports:        - containerPort: 80