You will need to have lived in New Zealand for at least three years prior to commencing your studies to be eligible for fees-free study.
To find out whether or not you're eligible, go the Fees-Free website and enter your details:
Change of residency
You will be eligible for fees-free in Semester 2 if you meet the Government's other criteria before the beginning of the Semester.
One of these criteria is that you must not have previously enrolled for more than 60 points (0.5 EFTS) of tertiary study; e.g. if you were enrolled for four papers (72 points) in Semester 1, you may not be eligible for fees-free in Semester 2.