@David
After looking on HP website for linux driver for that printer, you end up here:
It mentions that some Linux distros include HPLIP, but I do not know if that is true for Zorin.
I dont have a HP printer, so do not know if HPLIP is any help, or whether there is another (proven) solution.
There are dozens of supported HP printers listed on the HPLIP website, sorry too many for me to check if your one is included or not.