Which HP printer model are you referring to? What cartridge number?
Even a cave man knows that if a cartridge is still in the factory-sealed packaging, ain't nothing going to happen to it. Of course, if he stores it above the BBQ grill rather than the suggestions printed on the side of the box, then something adverse will happen to the ink. Follow the storage instructions and keep the receipt handy if a bad cartridge was bought.
If after the cartridge is installed and clogs up after sitting for a long time in the printer, then I do the following.
My Epson R1800 photo printer has a pad located beneath the print cartridges and heads when they are in their "parked" position. But, this applies to printers such as mine and maybe not to your model.
Per instructions, I apply a few drops of "Print Head Clog Buster" to the pad and let it sit overnight. Check out
Cleaning Cartridges for Inkjet Printers
This works for my printer when it sits a long time. It may not for yours.