With the release of the Office 365 May updates, a new setting has appear on SharePoint Online administration center.

This settings – called Top Navigation Bar User Experience – is available through the SharePoint Online administration center at the top of the Settings left section.

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This settings allows you to display/hide links to OneDrive for Business, Yammer/Newsfeed and Sites. You can not add additional links or hide Exchange Online link (Outlook, Calendar or People) if the user has an Exchange Online mailbox.