Sometimes, when you’re using a Linux server as your home router/Internet gateway, you need to change your public IP. I won’t go into the reason(s) why, because they don’t really matter. Maybe you accidentally exposed the proxy port (mostly just for your kids to protect their Internet access) directly to the Internet and ended up blacklisted by most things on the Internet, who knows? Best not to dwell on the hypothetical.
At first, it seems obvious: just release and renew with your DHCP client. A quick
dhclient -r enp4s0 (or whatever your interface name is) seems like the solution. But ISPs are too smart for that. Maybe try turning off your cable modem and leaving it off for a few minutes? Nope. None of this works because of how ISPs (and really, most any DHCP server) handle DHCP leases: they’re tied to the MAC address of your network interface. This means that when your network interface’s MAC address is seen by their DHCP server, it’ll offer it the same IP. This makes sense for ISPs to do; they can tie an IP to a customer based on their physical device.