@Palomino 

Like you said, your previous 8616 device was a pure modem, but your new replacement HG531 is not a pure modem, it should be a modem router.
You want to connect this device to the front of the 470, you first need to pay attention to the LAN port of the HG531 with a network cable to the WAN port of the 470.

Also if your ISP gives you the internet connection type that needs to be set up, then you need to set it up on the HG531 on the front end to ensure that the front end is able to access the internet normally, and after that select Dynamic on the WAN connection type on the 470.

There is another very important issue, because the default IP address of the 470 is 192.168.0.1, so you must ensure that this IP is not in conflict with your front-end HG531.
If the LAN IP of the HG531 is also 1292.168.0.1, you need to manually change it to another network segment, such as 192.168.1.1.

And if you connect like this, if I understand correctly, your network is double NAT, which is generally not recommended, especially when there is a need for open ports, VPNs, etc.