TL;DR: I imagine that there is a way to temporarily disable access to a pod / service so maintenance can be done. In this case: Block access to a database so a dump can be restored.
$ kubectl exec podwith-postgresql-59b77ffb7d-fc4xj dropdb dbname
dropdb: database removal failed: ERROR: database "dbname" is being accessed by other users
DETAIL: There are 10 other sessions using the database.
Just rescaling ReplicaSets to 0 or killing Pods didn't turn out successfull as Kubernetes (or Helm?) does a good job in bringing stuff back up.
Background: Specifically I was updating a Helm chart that depends on the Postgresql chart as a default database. I did my due dilligence and did an sql dump of the database before attempting the upgrade. And yadayadayada, stuff hit the fan and I would like to restore the dump, but since there was a new empty Database created and the application is already running I can't delete or replace the existing database as there are active connections to it.