How to implement DTAP in k8s?
Kubernetes supports namespaces. 


  multiple virtual clusters backed by the same physical cluster


These namespaces can allow you to use one cluster for all your environments. You can also do fancy things in your CI/CD pipeline so that each branch or each commit gets its own namespace. Those pods in prod namespace can still speak to pods in dev namespace unless you segment with NACL's. Just make sure you CNI supports that.

That being said most large companies I have worked for are running a cluster per environment.

I don't think there are right or wrong answers here. Do what you think is best for your company/team/workload/environment etc.