Netwatch...
/tool netwatch add host=1.1.1.1 timeout=15s down-script="/ip dhcp-client release numbers=0" comment="Monitor Cloudflare"
Obviously changing "numbers=0" for whatever interface this is on, and the timeout to what suits. You can also Log errors as you see fit. This is at a 1 second interval by default.
You can also write this to be added when you dhcp is bound - and then also remove when unbound (important). As to how - you'll have to research that for yourself (I recommend making one that suits - exporting and adding to dhcp-client script to simplify the process). Also you can do finds to get the variables you need - but I am deep in that hole ATM and have nothing to offer (apart from a search for comment is mostly doable).
V7 has more options for netwatch.