Employer wants me to sign a new contract with worse terms

An employer cannot unilaterally change your employment agreement. The Employment Relations Act 2000 requires good faith, and changes to terms need your agreement. If the employer proposes changes, they must consult you, provide relevant information and give you a reasonable opportunity to consider it, ideally with advice or a support person. You are not obliged to sign immediately. Threatening dismissal if you refuse can amount to unjustified action, and if the employer dismisses you for refusing, the dismissal may be found unjustified, unless there is a genuine business reason and a fair process was followed. Request the proposal and reasons in writing, seek advice from a lawyer or a union and put your response in writing. Continuing to work under protest is not necessarily acceptance of the changes.