I just did this. My flight was delayed 4 hours, and I went through the security checkpoint 3 hours after my scheduled departure time.
You might want to double check the security checkpoint will stay open as Zach Lipton suggested, but my airport told me the checkpoint will stay open as long as there are still departing flights (even if they’re delayed).
Also note that you’re still likely out of luck if you need to check in at the airline desk for any reason (to check bags for example), but if you’ve already checked in online and you don’t need to check any bags you’re fine to arrive late.
Also it’s a good idea to understand why your flight is delayed. If it is due to a mechanical issue and your plane is already sitting at the gate, you still probably want to arrive on time in case they resolve the mechanical issue sooner than expected.
If you’re still waiting on your flight to arrive at your departing airport, it’s probably a good idea to continually monitor its flight path and estimated arrival time in case it changes again.