Q: Please can you clarify my understanding on this subject.  If an employee is on Approved leave without pay for a period of time, how is the Annual leave treated:

No accrual for the period of leave without pay
Anniversary date is changed based on the period of the LWOP

Does the employee need to agree to this?

A: Leave without pay is an agreed term.  So, it is based on what was agreed when the leave was approved. For example, if an employee asks for 6 weeks LWOP and the employer agreed, the first week is counted as part of continuous employment by law (Section 16) but the other 5 weeks may have been agreed as a break in service or all to be counted as continuous employment.  Here is a reference from EmploymentNZ.

Taking more than one week
If an employee takes a continuous period of leave without pay for more than one week (not including unpaid sick or unpaid bereavement leave):

• their anniversary date for entitlement to annual holidays moves out by the amount of unpaid leave taken (not including the first week). This means the employee becomes entitled to their annual holidays later each year from then on, or
• the employer can agree with the employee that their anniversary date for annual holidays entitlement won’t change. If they agree to this, the employer must also reduce the divisor for calculating average weekly earnings for annual holidays by the number of weeks or part weeks greater than one week that the employee was on leave without pay.

Reference: https://www.employment.govt.nz/leave-and-holidays/other-types-of-leave/leave-without-pay/