The reason for your HP printer to be not able to print over the network as quickly as you expect because of various reasons. I will discuss a few troubleshooting techniques to resolve the issue, follow them carefully:
When you are printing over the network, the work is done on a priority basis and there are numerous other processes going on at the back end. So make sure to avoid adding multiple devices to your network at the time of printing. Also, ensure that your network is well connected.
Restart your Printer Setup
One of the most effective techniques for fixing minor issues is to restart your printer setup which includes your HP printer machine, router, and computer, wait for few minutes and see if the problem is resolved.
Update Firmware/ Driver
Most of your printer functionalities are controlled via these drivers and firmware. These are a software program which is vulnerable to get outdated or corrupted. So, head to your vendor's official website and download all available latest version of the drivers and install them.
One of the possible reason for your printer to print slow on the network can be attributed to a jammed printhead. Due to regular use and low maintenance chances are that your printhead might have been blocked or jammed. So open the top compartment and clean the printhead manually using a clean piece of cloth soaked in warm water.
Hopefully, these troubleshooting techniques helped you resolve the problem, in case you have any further doubt or query, feel free to reply back.