If you're feeling adventurous there's support for network filesystems like NFS, GlusterFS, CephFS, but I wouldn't recommend those for Postgres.
https://kubernetes.io/docs/concepts/storage/persistent-volum...
In one of his demos, Josh Berkus recommends just using the K8S ephemeral "emptyDir" storage type on each node, and counting on Patroni to maintain data persistence through replication. e.g. any one Postgres node may die and lose its local data, but when its replacement is created, it will be populated with a fresh copy of the database wherever it is scheduled on the K8S cluster. That sounds workable for smaller databases, though it gives every single person I've suggested it to nightmares.