SOLVED: How to Add a Contact Picture in Outlook Web Access (OWA) 2013

You can’t.  That’s blunt, I know.

The only exception to this is YOUR picture.  If you click your name (top right corner) a drop down will appear with a place holder for your picture and you can click CHANGE to set your picture.

If you want to add a picture / photo to a Contact you need to use a client like Outlook.