Are you contemplating adding the adapter to speed up printing, or have you got one already. Your post is not too clear. hwo is the printer connected right now?
If you connect a HP printer to a parallel port, make sure the port is set to ECP mode in the BIOS - printing can be pretty dire otherwise. My experience with HPs is that where possible a USB connection isto be preferred - do you have one - if not why not add one by way of a plug-in board. But before you do, what version of Windows are you using, as they don't all support USB.