I doubt you even own a Honda Clone with such a statement. A Gravity fed carb does not mean it has a primer!
The 6.5HP Honda Clone engine has NO primer. I know by hands-on experience because I have completely disassembled my clone's carburetor before. It has a choke, and a fuel shutoff. The fuel tank is mounted on the crankcase (higher than the carburetor), and the fuel flows by gravity into the fuel line down from the fuel tank, into the carburetor bowl, thus NOT requiring any primer to start the engine, because the carb bowl is always full of fuel. .............AKA Gravity-Fed Carburetor
A typical Briggs & Stratton push mower has a primer, because the carburetor uses suction to draw fuel up from the tank, it's NOT gravity fed, and has no float or bowl. I have a 3.75HP Briggs engine like that.
A lot of the new gravity-fed push mowers don't even have choke or Primer, like my Father's 6HP one.
The Thread Starter asked if his Honda Clone engine has a Primer. I have 100% experience to say it does not have a Primer. The question has an answer.