Do you mean static IP for locally, or static IP for the Internet?
Because if it's just local, you can configure the static IP directly on the server/VM/whatever and bypass the router's DHCP entirely. Just make sure to assign it an IP that's outside of the range the router will assign and you'll be golden.
As for the Internet IP, the best solution for that is usually some sort of DDNS service to make sure your domain always tracks your public IP.
Also, Cloudflare tunnels, cheap VPSes.