The Google Phone app is being updated in the Google Play Store, bringing a new chat head feature and improved persistent notification shade. The new build is version 17.0.184919600 and will come to compatible devices (Google Nexus & Pixel phones, Android One phones, etc) over the next few days.
The main new feature is a chat head feature. Now, when you are in a call and move away from the Google Phone app, you will have a chat head, similar to Facebook Messenger, appear on your Home screen. Tapping that head will allow you to control the call: Return to the call, mute the call, move the call to speaker or hang up. There is nothing you have to do to enable this feature and you can move the chat head around your Home screen to a convenient place.
The idea here is to make it easy to return to a call after you have gone to another app during that call. For example, you need to check your calendar to confirm a meeting time.
As part of this update, there is also an improved persistent notification shade too. That shade allows you to end a call as well as move the call to speaker without actually having to go back into the Phone app.
Look for the update to come to your Nexus, Pixel or Android One device soon. Having played with this new feature this morning, I can see where I personally am going to be using the chat head feature a lot during my day-to-day.