This appears to be quite an old panel. This one was manufactured with a single ground / neutral bar. I can't see in your photo, but if it is mounted on an insulating material there should be a green screw bonding the bar to the panel itself. This is the Main Bonding Jumper and there can only be one of them in the system. (The bar is probably mounted directly to the panel as the panel is designed to be the main panel.)
According to the National Electrical Code there can only be one point in the electrical system where the neutral and grounds can be joined. (There are rare exceptions but they are none of your concern here.) That one point is considered the entire main service panel in a residential installation. You can have multiple common bars in that one panel and does not need thea bonding screw for additional bars.
You can add another ground / neutral bar to the panel if you desire. You can add it on the left or at the bottom if there is room. Look for a Ground Bar Kit that is designed for this panel. Or if they no longer make them for this panel you should be able add a generic ground bar by drilling and tapping the panel for the mounting screws of the ground bar kit you purchase. DO NOT use zip screws for this mounting.
Stay Safe!