Clarity

 How to get the “new from template button” for a resource in the projects screen. ?

There is an access right that you can assign to an user on a global level: "Project - Create from Template"
Assign that to one of your test user, and see the changes when you go to Home --> projects page.

Hope that will answer your concern. 

A small clarification in addition to Abhisek's reply ... in all the systems that I use, when I give users the Project - Create right, they automatically get BOTH "new" buttons; the New and New from Template buttons.

The Project - Create from Template is a right that you can give instead of the Project - Create right, to only allow users to create projects from a template. At that point the users only see the New from Template button.

To answer the original question, you do not state if you see the New button, but if you do see New then I am not sure why the New from Template button is not available. Unless there has been a customization in your system to remove it.

Which version of CA PPM are you using?

Thanks for clarifying the Access rights in details, Sue. But in this case, Kaustubh did not mention if the "New" was at all visible for the user or not. 

However, I have seen a lot of organizations who do not allow the users to create project from scratch. They only prefer them to use the existing Templates to be used by the Project Managers. This might be the same case for Kaustubh also.