It looks like you can close the report but not the print preview window. The good news is that the user is actively staring at the screen at that time.  My suggestion is to have a button for direct print and another for preview.

call one print and the other view

If you want that type of functionality directly on the ribbon, I believe you would have to create a custom ribbon button with a callback function that gives you that functionality.

In Access Developer 44, Richard goes into detail on how to create custom ribbons and buttons as well as assigning functions to them.

Alternatively, you could create a small popup form that would open along side of your print preview. This form could have buttons that would mimic the effects of the ribbon. For example, there could be a "Print & Close" button that does what you want, and then a "Close Preview" button that the user could click instead if they just want to close the preview without printing. Clicking either button would also close the popup form.

While not as neat and tidy as using the ribbon, this method might be easier to implement.

Yeah, Donald hit the nail on the head. In order to do that, you would need your own custom button, which you could put on the ribbon, the Quick Launch Toolbar, or your own main menu. Personally, I lean toward the main menu option or maybe a print menu.

And I would create a print and close button where you can print it and then have it auto-close because there's no way to build that functionality into one of Access's existing buttons. You'd have to make your own button. But you could make, like Donald suggests, one button to preview it and then a second button to print and close.

And you could certainly put that on the ribbon, but as I show in Developer 44, maintaining or creating your own custom ribbon isn't exactly easy. I wish the Access team would make it easier, but it just involves a lot of work.