If you leave a job - voluntarily or involuntarily you can still contribute to KiwiSaver. If you're going to a new job fill in the KiwiSaver deduction form and hand it to your new employer.
If you're not going into a new job you can still make voluntary contributions at any time. Contact your KiwiSaver provider and talk to them about your situation.
If you're no longer eligible to be a member with your current KiwiSaver scheme provider, then you'll move to a new scheme.
If you work in a state or integrated school, the Board of Trustees is your employer for KiwiSaver purposes. If you change schools, you're treated as starting new employment. If you're not already in KiwiSaver you will be automatically enrolled even though you stay on the same payroll.
Working more than one job
If you start working a secondary job:
contributions should be deducted from any new jobs you start, as well as your main employment
all your employers will make compulsory contributions.
If you make regular contributions directly to your KiwiSaver scheme provider and you stop working, check with your scheme provider to see if you can stop your contributions.