Thank you for your patience here and apologies for the delay.
Do I need to deploy a new subnet and node pool for each zone?
Your understanding here is correct, below is the response I got from the team.
Currently, a single NAT gateway cannot support multiple zones. For a multi-zone architecture with NAT gateway, I would recommend creating 3 separate node pools per zone and assigning each to their own subnet. Each subnet can then be attached to a NAT gateway assigned to the same zone. To use a multi subnet setup with AKS, you can read more here: Create node pools in Azure Kubernetes Service (AKS) - Azure Kubernetes Service | Microsoft Learn.
Meanwhile please feel free to upvote this feature request for Zone-redundant NAT Gateway.
Please let me know if you have any further questions and we will gladly continue with our discussion. Thank you!
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