The basic board spec shows it does not have a Serial port. However it does have an Intel Management Engine interface for which the drivers should be here.
If you read the driver page it informs that if these drivers are not installed it shows as missing drivers for a Simple Communications controller.
To be clear serial ports are legacy devices and seldom used today. If not actually needed the lack of drivers for this specific device would have no effect on the system
Hp Z420 Drivers Windows 10
The specification also says nothing about a parallel port (Lpt1). Do you have an expansion card into which you plugging in the printer. The socket would not be in the main group of connectors but separate and in the vertical slots. Some port expansion cards had both Serial and parallel ports so this might be the missing driver. If so you would need to identify what the card is and find the appropriate drivers. Unfortunately it is highly likely they would not be available for Windows 7.
Hp Z420 Pci Serial Port Driver Windows 7
Hi I just installed fresh copy of windows 10 on HP Z420 i notice in device manager missing PCI Serial Port i went to HP drivers support tried the following drivers with no success Intel Chipset. This page contains the driver installation download for PCI Serial Port in supported models (HP Z420 Workstation) that are running a supported operating system. I think I'll leave it alone for now. I've researched what PCI Serial Port is for. I'd say it could relate to the PS/2 ports as well as another one similar to the VGA port, none of which I use. Maybe the dial up Com port as mentioned but I can't tell if I have one. I tried that driver link but I got.
Hp Z420 Drivers
The spec of the Printer does not show USB so have you got a USB to Parallel converter, In which case that is going to need drivers itself. Venerable and functional it may be but the 710c is a very old printer and although it may work if set up right is not supported on Windows 7.