Not anytime soon is the short answer.
The Prime Minster recently said that her government is considering allowing people who are fully vaccinated to enter to boost tourism and foreign investment. However, there is more science to pass under the bridge before any decision is made, including whether people already in New Zealand must first be fully vaccinated (scheduled to be completed by the end of 2021).
As the pressure comes off places in managed isolation the government has opened a small number of places to construction workers, international students, and fruit pickers.
The government is set to review immigration policy settings. The Productivity Commission is due to report back in April 2022 on an immigration enquiry. But expect more changes in the meantime including new categories of border exemptions.