Using New Outlook on Windows for personal email, calendar, and contact management
To better understand the issue, when you click People on the left navigation do you see All contacts under the account? What is the domain of your account e.g. @outlook.com, @msn.com, @live.com, etc.?
Also, to double check, if you click Settings on New Outlook top navigation do you have one or more accounts? It may matter if there are multiple if the main account you want to add the contacts is not marked as Primary.