Which HP 4210 do you have?
There's a C4210, and an F4210, and maybe 2 or 3 other HP models that all have the number 4210 as part of the model number.
What version of OS X do you have?
Have you checked for updates to Apple's HP drivers?
Is your printer USB only, or is there also an ethernet (network) connection?
If USB only, does the printer finish a page when the printer is plugged directly into the USB port on your MBAir?
I'm asking that to find out if it ALWAYS fails to print a full page, or only when plugged into the USB port on the TC?