How to add new contacts to an outlook.com account in an Android device?
There is another workaround which involves a handy third-party tool- Contact Editor Free.


  This editor is a replacement/alternative for your native editor and
  it's invoked in the same way. It will be started whenever you try to
  edit or create a contact (and you select "Contact Editor Free")


When you use the regular Contacts app to create a new contact, it gives you the alternative option to use this application, which gives you the option to add either a gmail.com or outlook.com contact essentially overcoming android's limitation to add outlook contacts.

One user mentions a minor drawback:


  The only drawback to the Contact Editor Free solution that I've found
  is that I can't delete contacts from the outlook.com account this way.
  That's a pretty minor problem, however, since deleting contacts is
  something I do a lot less often than adding them.


Acknowledgements


How to add contacts to my outlook.com account