Overlay networks are typically set up as new network (greenfield) sites, but a completely new network in isolation is not useful, unless there is a planned big bang migration of all applications, which means migrating every application from the legacy network to the new network in a single migration.
If instead a staged application migration is chosen, where only a percentage of applications are migrated to the network, then the new overlay network will need to communicate with the legacy network and be required to operate in a brownfield setup.
A brownfield setup normally means applications are migrated in stages to the new platform, as opposed to all in one go, which builds confidence in the new network and new technology associated with that network. When moving applications to the new platform, it will typically involve performance testing the migrated applications in the new network, prior to throttling live traffic...