Work permits and visas and such are handled very much on a case by case basis. Your best bet is to talk directly to your embassy. Where are you from originally? Have a look at our page on work permits in Italy for some more information.
Hope this helped!
Since work permits are handled by employers, yes, you will probably need a new Nulla Osta when you change jobs. It will be best to talk to your new employer and go to immigration to find out what you need to do.