Consul service check definitions hardcode tags... Like technically you are supposed to tag services with stuff like "primary" or "replica" to be able to filter during service discovery. You can override them with a CLI command. If repmgr has an option to execute something after automatic failover is triggered, then you could update the service tags; then the rest could be done with consul-template.
Aha, I guess you could pack that into promote_command? There's also failover_validation_command but it seems less suited.