As there are no buttons on the Narrative Clip 2, the Narrative Clip 2 is technically always on. You can put it into a "sleep" mode by placing it facedown. This will save your Clip 2's battery.
To check if your Clip 2 is still taking active, you can double-tap it. If the LEDs light up your Clip 2 is taking photos / videos.
If you have double-tap disabled on your Clip 2, you can check if it's active through the "My Clip" view in the Smartphone App.