You can set Netflix to automatically play the next episode in a TV series.
From a web browser, go to your Account page.
Open the Profile & Parental Controls settings for the profile you want to use.
Select Playback settings.
Check Autoplay next episode in a series on all devices.
To stop autoplaying the next episode, uncheck the box.
You may need to refresh your device to pick up the updated settings.
Switch to another profile, then switch back.
Or, sign out of your device and sign back in.