What you need is a so-called PostgreSQL Kubernetes operator that will be responsible for building Kubernetes objects based on your requests.

You can have a look at OperatorHub.io, they have some PostgreSQL operators.

Maybe an easier solution is KubeDB and the KubeDB PostgreSQL implementation.

The operator will also create a Kubernetes Service that will create a resolvable name linked to the Kubernetes Pods of your PostgreSQL cluster. KubeDB doc explains how to connect to the database in their documentation.

Now coming to your question :

Is it possible to establish connection from my localhost app [...]

You can access the Kubernetes service from outside but you will have to create a Kubernetes Load Balancer. See this blog article which explains it in details.