Hello @Wen Rui Zhao - (OPS) ,
Thanks for reaching out to Microsoft QnA Platform!
There is no limitation on outbound traffic from a private AKS cluster.
In a private cluster, the control plane or API server has internal IP addresses that are defined in the RFC1918 - Address Allocation for Private Internet document. By using a private cluster, you can ensure network traffic between your API server and your node pools remains on the private network only.
Have you followed any specific document to create the private AKS cluster such as this - Create private AKS cluster ?