Microsoft has made official Outlook extension available for the Microsoft Edge now. The extension is now available and can be installed by clicking on the link below.

The extension adds the outlook icon in the top bar, clicking on which pops up a window. This window allows you to perform various outlook mails related actions without opening a new tab. The pop-up window can be made to disappear just by clicking anywhere else.

Install link

Details:

Send and receive email, manage your calendar, tasks, and more without opening a new tab.

The Microsoft Outlook browser extension brings you the power of mail, calendar, contacts, and tasks using an icon in Microsoft Edge. Quickly access your Outlook work account or your Outlook.com or Hotmail account without switching to another tab or app.

Features
  - Access work or personal accounts
  - Read, send, and manage email and get new email notifications
  - Create events, view upcoming ones, and join online meetings
  - Create, track, and manage tasks
  - Manage contacts  

Great for doing all this without switching tabs or apps
  - Reading an important email 
  - Checking your calendar 
  - Adding a task based on what you’re reading on the web
  - Fast look up of a contact’s phone number
  - Referring to info on a webpage while writing an email