Hi,
Create the new VM and make sure you set it to use the same Virtual Network and subnet as the old VM.
In the portal, navigate to the old VM -- Networking -- Network settings blade, then on right, click on network interface/ IP configuration. This will take you to network interface -- IP configurations. Next click on the IP configuration (often named "ipconfig1") to edit it.
Set Allocation to Static and change the private IP address to something different. Click Save. Restart the VM so that the IP address change will take effect.
Now repeat the above process with your new VM, and set the private IP address to the previous private IP.
Please click Accept Answer and upvote if the above was helpful. If something is unclear add a comment below.
Thanks.
-TP