Step 1: add curl to your container image REF, Hint: Modify the Docker file to include curl.
Step 2: (in kubernetes deployment) configure the resource to mount the certs needed to query (GET request) the REST endpoint. REF Hint: Follow the way serviceaccount credentials are mounted to a POD.
Step 3: Now use those certs which are mounted to your container. In the liveness probe to curl it the way shown here
At this point if you have curled successfully with status code 200. you will have a linux comand execution code 0 which lead to successfull liveness check else the pod will be restarted.