Power supplies don't push electricity into the components (motherboard, graphics card, HDD, ODD, etc.)... instead electricity is drawn from the power supply based on the demand of the components. So, YES, you can and must install a more powerful PSU (power supply unit) in your computer for it to function correctly with that monster of a graphics card you installed.
I suggest getting a Corsair CX500 or CX600, as they come highly recommended and are known to fit many HP consumer desktop cases including yours. If you wish to ease cable management somewhat, you might consider getting the CX500M or CX600M power supply. These are identical to their non-M brethren and cost a little extra but help with cable clutter concerns.
Please send KUDOs