Missing the Health.app on my iPhone?
Go to Setings > General > Restrictions and enable it.

Do nothing and re-enable it, the app should be back. On iOS 10 and later, you might also need to go to the App Store and reinstall system apps so be sure to try that as well.

Last - look for any profiles in settings in case someone managing your device has prevented use of that app systematically. You can generally remove the profile or ask them to reassign your device if you should have access to the health app and store health data on your device.