You can use Istio for implementing mTLS. You need to install Istio in your Kubernetes cluster.
Istio is an open-source service mesh that layers transparently onto existing distributed applications. Istio's powerful features provide a uniform and more efficient way to secure, connect, and monitor services. Istio enables load balancing, service-to-service authentication, and monitoring ?with few or no service code changes. Its powerful control plane brings vital features, including:
Secure service-to-service communication in a cluster with TLS encryption, strong identity-based authentication and authorization.
Automatic load balancing for HTTP, gRPC, WebSocket, and TCP traffic.
Fine-grained control of traffic behavior with rich routing rules, retries, failovers, and fault injection.
A pluggable policy layer and configuration API supporting access controls, rate limits and quotas.
Automatic metrics, logs, and traces for all traffic within a cluster, including cluster ingress and egress.
Reference:
https://learn.microsoft.com/en-us/azure/aks/istio-about