Hi,
The HP ENVY 6455e All-In-One Printer is listed in About AirPrint - Apple Support as a model with support for the driverless AirPrint technology, so you should be able to use this printer without having to install drivers. This provided that the printer and the computer are connected to the same network (Wi-Fi router).
To begin with, you may want to try the following procedure in the exact order:
Power off the router/modem, the printer, the Mac, and all other devices/computers. Wait two to three minutes. Power on the router/modem. Wait two to three minutes. Power on the printer. Wait a minute or two. Power on the Mac. Finally, power on all other devices/computers.
Reset the Mac printing system to solve a problem – Apple Support (UK)
Add a printer on Mac – Apple Support (UK)
Software/drivers from a printer manufacturer may or may not add functionality, and may be needed for a USB printer connection.
However, it is also possible that a printer manufacturer provides extra software (for setup, ink management, and similar purposes) with higher system requirements than actually needed for printing. This could lead to difficulties for a user of an older operating system. If so, one may have to try a manual setup (for example, using WPS) instead. It may also become necessary to abstain from using a time-limited free ink service, et cetera.
AirPrint as such should be usable with Mac OS X 10.7 Lion and higher.
The ability to print using AirPrint could also be tested through an iPhone/iPad.
Use AirPrint to print from your iPhone, iPad, or iPod touch - Apple Support
Information about the Wi-Fi router make and model would help (please do not post any serial numbers or access codes, though).