Is there a method that works like start fragment for result?

All of the Fragments live inside Activities. Starting a Fragment for a result doesn't make much sense, because the Activity that houses it always has access to it, and vice versa. If the Fragment needs to pass on a result, it can access its Activity and set its result and finish it. In the case of swapping Fragments in a single Activity, well the Activity is still accessible by both Fragments, and all your message passing can simply go through the Activity.

Just remember that you always have communication between a Fragment and its Activity. Starting for and finishing with a result is the mechanism for communication between Activities - The Activities can then delegate any necessary information to their Fragments.

If you wish, there are some methods for communication between Fragments,

setTargetFragment(Fragment fragment, int requestCode)
getTargetFragment()
getTargetRequestCode()

You can callback using these.

Fragment invoker = getTargetFragment();
if(invoker != null) {
    invoker.callPublicMethod();
}