I have a new print server added to Server Manager but Print Management is missing from the context menu when I right-click on the server. I can access Print Management from the Tools menu in the top right corner of Server Manager window. Is it possible to add it to the print server's context menu as well?

Hi,

According to your description, my understanding is that you want to open Print Manager by right-click print server.

As Windows Server 2012, we open the Print Management Console by opening Server Manager - Tools - Print Management. I am afraid that the right-click context menu can't be manually added.

You may reference link below for more information about  Configure Print and Document Services:
https://technet.microsoft.com/en-us/library/jj134163.aspx

Best Regards,
Eve Wang