No, unlike the ink that is used on inkjet printers, toners from laser printers don't dry up even if you leave them for a long time.

How long do laserjet cartridges last?

The shelf life for an original printer cartridge is 24 months and the shelf life for a compatible cartridge is 36 months. Over time, ink dries out and settles inside the cartridge, which can cause your printer to clog.

Can HP ink dry out if not used?

Cartridges can dry up if they are not used properly. To get the most out of your printer cartridge, make sure it remains sealed and is stored upright in a cool, dark space like a desk cupboard. Once installed, be sure that you run a print job at least once every couple of weeks to keep the cartridge primed.