1) Conduct basic checks on your controller and headset. Once you find the microphone can't work on your Xbox One, try looking for the issue and troubleshoot it.
2) Make sure your headset is not muted. Check the mute button on your headset control or the audio settings on your Xbox One. (If none of these work it might be your controller isn't compatible with those headphones and you can get a new controller or headset, if you don't, you can also use the Xbox App on your mobile device or computer) Hope these work.