Problems installing new printer HP Officejet Pro 8210

If you follow this link, https://support.hp.com/gb-en/drivers/selfservice/hp-officejet-pro-8210-printer-series/7902063 you can see that according to HP it is supported in Mac OS X Mavericks

make sure the Detected Operating System is Mac OS X 10.9, there is the HP Easy Start

which you probably have and also a Firmware download you may want to install.

The big question is why are you still running Mac OS X 10.9.5 Mavericks, your mac is capable of running the latest macOS Catalina, but don't go there quite yet. It is a cold, dark place.

Your mac can upgrade to High Sierra or warm and fuzzy Mojave.

How to upgrade to macOS Mojave - Apple Support

How to upgrade to macOS High Sierra - Apple Support

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

If you are considering upgrading to Catalina be warned that it does not support 32bit apps.

Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,

some updates may be free, some may be paid. Use this app to discover which apps you have

are 32bit, https://www.stclairsoft.com/Go64/. Once the list has been created you can then

contact the developers of the apps to see if they provide 64bit updates. 

How to upgrade to macOS Catalina – Apple Support

That is a really old version of macOS and the driver for the new printer may not work with it. You really should upgrade macOS to a later version. Your laptop can support the current macOS 10.15 Catalina as long as you don't rely on any 32bit apps.

Apple article regarding Catalina and 32bit apps support:

https://support.apple.com/en-us/HT208436

At a minimum you should upgrade to macOS 10.11 El Capitan, but even macOS 10.11 is unsupported by Apple now. If you are unsure about 32bit app support with Catalina, then you can safely upgrade to macOS 10.14 Mojave instead as Mojave is still receiving security updates from Apple and it should support your new printer. With Mojave you really should not need to install any software from the HP CD.

Check out this Apple article which includes links to download various versions of macOS from 10.11 to 10.15. I've seen reports on these forums that sometimes macOS 10.11 is first required before you can upgrade to later versions such as 10.12+.

https://support.apple.com/en-us/HT201372

Just make sure to have a good working backup before you upgrade to a later version of macOS just in case something goes wrong.