Welcome to the home of HP's Linux Imaging and Printing software (HPLIP).
Chances are, your Linux system already has the HPLIP software installed. That's because all major Linux distributions regularly pick up the HPLIP software and include it with their distribution installation. However, if it is not installed or you need to upgrade to a newer HPLIP version to support your printer, you've come to the right place.
On this website you can download the HPLIP software which supports 2516 HP printers on nearly any Linux distribution available today.
The current version of the HPLIP solution is version 3.16.2. (Release Notes)