In my recently replaced Android phone I got a small Gmail logo in the top left corner of the screen whenever I got an email. I have just bought a replacement phone and I cannot remember how I got this function up and running.

I've been looking at some apps but none of them do just this one simple thing (it's always  lot of other stuff included that I don't need).

Any tips would be appreciated.

Did you have the app "Unread Badge (for Gmail)" installed on your old phone?

 

 

While it depends on the version of android installed, what the manufacturer implemented, and the version of gmail installed...

 

on the android HOME screen open android SETTINGS

tap on Notifications

tap on Gmail

make sure 'Block all' is not enabled

taping the cog wheel 'settings' icon here should take you the the gmail in app settings menu

 

In gmail,

open settings

tap on your email name

make sure 'Notifications' is checked on

 

tap 'Inbox sound & vibrate'

set your notification preferences

 

...also, the phone manufacturer may have customized how the notification bar at the top of the screen functions.  They may have included an app to change how the preferences work.  Sometimes this is kept separate, and other times is part of the 'Launcher' home screen preference settings. 

In GMail, Settings, choose account if more than one, tick Notifications, tick Sync Gmail.

 

In Inbox sound & vibrate, tick Label notifications.

 

You can customize ("Label") notifications, I think, so create a Priority Inbox and just get notifications for those specific emails.

 

(The above apply to my phone running Stock Android 7.1.1/May 1 security release.)