The latest iOS update, iOS 13.7, just rolled out and the big new iPhone feature is a COVID-19 tracking system. It utilizes the contact tracing technology that Apple and Google have been working on for the last several months. If turned on, it lets you know if they've been in contact with or in close proximity with somebody has tested positive with COVID-19. And there's no need to download a separate app.
Once your iPhone is updated with the new software, the Exposure Notification Express system will be turned off by default. To receive these push notifications, you'll have to turn them on. To do this, you'll want to make sure your iPhone is updated with iOS 13.7, and then you'll need to go into Settings, scroll down and find the label that says "Exposure Notifications." Then select "Turn On Exposure Notifications."
Naturally, if turned on, this new feature will require your iPhone to collect more information about you and your surrounding area, which could leave you with questions related to privacy. However, Apple says that it's "not collecting or sharing exposure notification data with anyone." And if you Exposure Notifications turned on, information related to your exposures can only be shared with your permission.