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Interim name suppression has lapsed for William Willis (35) and Hannah Rawnsley (26), who police say crossed the Level 4 border from Auckland using essential worker exemptions before driving to Hamilton Airport on Thursday.
They took a commercial flight to Queenstown via Wellington, rented a vehicle and drove to Wanaka.
Police said they were notified via the Covid-19 compliance reporting tool online, and found the pair on Saturday afternoon.
Mr Willis is the son of Auckland district court judge Mary-Beth Sharp.
In a statement the pair said their actions were "completely irresponsible and inexcusable''.
"We are deeply sorry for our actions and would like to unreservedly apologise to the Wanaka community, and to all the people of Aotearoa New Zealand, for what we did.''
They confirmed they had tested negative for Covid-19 prior to crossing the border, and on their subsequent return to Auckland.
They were not considered close contacts and had not visited any locations of interest.
Interim name suppression lapsed for the pair at 7pm, and they did not seek further suppression.
"We initially sought name suppression after receiving death threats and we had genuine fear for our safety,'' they said.
"However, we remain committed to taking responsibility for our actions and will not be seeking further name suppression.''
In a statement Judge Sharp said like the rest of New Zealand, she was appalled by the actions of her son and his partner.
"In addition, I was and am highly embarrassed,'' she said.
"Had I known of their intentions, which of course I did not, I would have told them not to act so thoughtlessly and selfishly. I do not condone their conduct.''
She supported their decision not to seek further name suppression.