NAT Gateway is an enterprise-class VPC Internet gateway that provides NAT proxy services (SNAT and DNAT), up to 10 Gbps forwarding capacity and cross-zone disaster tolerance.

As an Internet gateway, public IP addresses are required to make NAT Gateway fucntion normally. After creating a NAT Gateway, you can bind an Elastic IP Address (EIP) to the NAT Gateway.
Note If your account has purchased a NAT bandwidth package before January 26, 2018, you still need to use the bandwidth package to provide public IP addresses. To associate an EIP to the NAT Gateway, open a ticket.

If you want to use the Internet Shared Bandwidth function, you can add EIPs to the existing shared bandwidth in the EIP console or buy a shared bandwidth first and then add the EIPs to it. For more information, see Add EIPs to Internet Shared Bandwidth.