Creating new async tasks
I would start by trying to make a separate package for making the requests, something like a presenter(MVP pattern - MVP in Android). 
Because, the way you have it now, it is hard to be tested and inside of the activity you have more logic, breaking a bit the SRP principle( SRP ).

Now, all it is left to do is to connect the activity and the presenter and that you can do using a callback.  
Also, as a bonus, all the stuff you need, presenter, etc, you can add to a dagger module.