Netflix have updated the Android version of their TV and Movie streaming app. The change is a new “Post-play” mode where it will go on to watch the next episode of a TV show at the end of the current episode just as other versions have. On a tablet you also get a new post play option for movies as well.
You can find the updated app in the Google Play store.
The new “Post-play” experience makes it easier to continue watching at the end of TV episodes (phones and tablets) or movies (tablets only).