Session disconnection when rollout Deployment's pod

Hello,
I’m a student currently studying Kubernetes.

While learning, I came across a question related to sessions that I hope you can help me with.

Here’s the situation:
After establishing a TCP socket session through an existing pod, I performed a rollout restart on the Deployment that the pod belongs to.

The Deployment is configured with minReadySeconds, so newly created pods are only considered ready after they pass health checks.

However, during this process, the original pod entered the Terminating state and the active session was disconnected. As a result, my application experienced a brief reload or disruption.

My question is:
Is there any way for a newly created pod to take over the session information from the terminating pod?