Pop up alerts like Installed new hardware and such like, try this and see if this helps.
First of all:
Go into the printers software manager and see if there is an option for notifications.
Alternatively:
1: Open Security centre.
2: Left click on "Change the way Security Centre alerts me".
3: You'll see a dialogue box with three options, click on "Don't notify me but display the icon".
If the above doesn't work then your best bet is maybe obtain the latest drivers and software for your printer, but if that isn't available then contact HP.
There is one more solution and that's to turn off your printer when not in use.