Lets say that your ISP has allocated you an new block - 188.8.131.52/28. When they allocate these addresses they will ensure they route them to the outside interface of your ASA. So anyone trying to get to one of those adresses will end up at the ASA.
You simply use the new addressing in NAT statements on the ASA eg.
I am a bit confused about your environment and your requirements. Like Jon I assumed that the way to use the addresses was to translate. But if I am understanding correctly your response you are not translating addresses but have the public addresses used directly on PCcs or servers in your network. If that understanding is correct and if you want to do this also with the new address block, then it would make sense to create a VLAN interface and assign the new address on the VLAN interface.
If you have created a VLAN interface on the ASA, have you also created the corresponding VLAN on the switch to which the ASA connects? And do you have hosts in the VLAN with addresses configured from the new address block?
In my outside interface i have a private address ip like 192.168.1.1 and the first block of public address is assigned to my inside interface eth0/1.
This sounds backwards to me. What is the gateway that your hosts use? The public address that's assigned or the private address of 192.168.1.1? Do you have any other devices in front of the ASA like a router?
Thank you for the additional information. If you have associated the new address block with the VLAN interface on the ASA then the VLAN needs to be configured on the switch and the hosts with the new addresses need to be in that VLAN. This would be a requirement to get the new addresses to work in the approach that you have started.
Without hosts in that VLAN and without that VLAN configured on the switch then it can not work.
This document gives several answers on frequently asked questions for PFRv3 channel state behavior.
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