In elasticsearch.yml I have set up the following configurations.
xpack.security.transport.ssl.enabled: true
xpack.security.transport.ssl.verification_mode: certificate
xpack.security.transport.ssl.keystore.path: certs/elastic-certificates.p12
xpack.security.transport.ssl.truststore.path: certs/elastic-certificates.p12
The certificates were generated from the steps mentioned in the below page
But to generate a client certificate we used the steps mentioned in the below link.
under Creating a client certificate.
So I believe its the same CA that signs both certificates that are configured in ES as well as the client certs. And I think that is why kibana is working with Elasticsearch. Because both are signed with the CA elastic-stack-ca.p12.