Entering tags from the "New Post" page

On some themes I've installed, there is a place to enter tags right from the new/edit post page (see screenshot). On a theme I set up for a blogging client, however, the option is not there. As a workaround, I can write the post, go back to the "all posts" page and select "Quick Edit" and do it from there, but it's just more work.

Am I just missing something or is this something that I can add myself to the "New Post" page? Is this option defined by a theme, or WordPress?