First, make sure your controller has fresh batteries. The Xbox One console is set up so the mic audio will turn off if your batteries are low in order to conserve power within the controller.
If your headset is connected direct to the controller via 3.5mm give the following a try:
- Disconnect the headset from your controller
- Fully power down your Xbox
- Power on the Xbox
- Sign into your profile
- Connect the headset back to your controller.
- Verify the headset itself is not muted.
- On your Xbox one controller double tap the Xbox button
- Scroll to the settings icon.
- Make sure the setting Headset mic is set to on.
- Adjust the game and chat mixer settings.