To connect Calm to the Apple Health app, please do the following: Open the Calm app and go to the Profile screen by tapping the icon in the top left corner of the home screen. Scroll down the page to get to Settings, and you should see an Apple Health option. Tap that option, and you'll be able to connect Calm to the Health app.
You can also find Calm under the 'Mindfulness' category in Apple Health.
You can read more about the Health app here: https://support.apple.com/en-us/HT203037