how to replace gmail with the new inbox by gmail
Enable notifications for Inbox:


tap menu icon
tap settings (just above Help &amp; feedback" at bottom of screen
tap your email address
check "New messages" and your choice of Vibrations, Lights, and sound.
Tap "Turn off Gmail notifications" &amp; confirm (if displayed)


Disable notifications in the Gmail app (if "Turn off Gmail notifications" is not displayed in Inbox):


swipe from left to right to expose mailbox list, labels, and settings
scroll down to "Settings"
tap your email address
uncheck "Notifications"


(repeat for each email address if you have multiple set up).
You'll be able to see your mail from either app, but notifications will now come from Inbox instead of Gmail.