hpsysdrv.exe is a utility from HP which monitors how many recoveries have been made in Microsoft Office suite. This is a non-essential process.
Disabling or enabling it is down to user preference.
Non-system processes like hpsysdrv.exe originate from software you installed on your system. Since most applications store data in your system's registry, it is likely that over time your registry suffers fragmentation and accumulates invalid entries which can affect your PC's performance. It is recommended that you check your registry to identify slowdown issues