You would need to contact INZ with details of the new job you want to take. They would need to check out that it was equally skilled, and that you have the necessary qualifications for it. Then, depending on the details, you might be given a variation of conditions, changing the employer mentioned on the same visa, or you might get issued a new visa with the new employer's name on it. (More discussion on this here.
http://www.enz.org/forum/showthread.php?t=42933) If you are being offered a permanent contract, or a longer one, a new visa might be issued for a longer time.
It is important to sort out the visa BEFORE you go to another company. On your present visa, it would be illegal to work for anyone different from the employer named.