For your app this would be the CoreLocation framework. You have to implement the CLLocationManagerDelegate protocol. With this you can track location updates. But in the end it all comes down to the permission the user has set in your app. From your post I get that you found that already.

If you want to track a third person with your app which uses your service you probably have to set up your own backend service where the data is sent to and where you then can query it. I don't know of a service which Apple provides for this use case.