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William Willis, a former New Zealand representative, admitted to breaching alert level 4 rules in his trip south on September 9, alongside lawyer Hannah Rawnsley.
Equestrian Sports NZ chief executive Julian Bowden said Willis' participation in future events would be discussed at the organisation's monthly board meeting on September 30.
Bowden wouldn't be drawn on whether he believed Willis should be allowed or barred from competition, saying the decision would be made by the board.
While he did note the complexity of punishing someone for behaviour outside of the sport, Bowden said it was clear to all Kiwis that Willis had made a serious mistake.
"New Zealanders aren't silly, he's an individual who's made a really bad call.
"I'm disappointed that anybody's doing it ... it's not a great look for anybody."
Bowden clarified the incident had nothing to do with equestrian sports and that the national body wouldn't ask competitors to breach travel restrictions in any way.
It comes after Law Society president Tiana Epati confirmed the matter would be looked into to determine whether Rawnsley misused a travel exemption document provided to lawyers to get through the alert level border.
Epati said lawyers were provided with an official letter to travel to priority court hearings. She said this was the only travel permit provided to lawyers, who were not essential workers.
"We don't really know that there's anything else she would have been able to point to. And if that's the case, that she has used her lawyer status to get across the border, then I join probably all of the legal profession in being extremely disappointed," Epati said.
"If any lawyer was proved to have misused this letter, not only would that be considered a disciplinary matter but they will have let the entire legal profession down."
Willis (35) and Rawnsley (26) issued an apology on Tuesday after declining to continue pursuing name suppression.
"The decision that we took to travel to Wanaka last week was completely irresponsible and inexcusable," their statement said.
"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.
"We can confirm that as part of routine testing for essential workers when crossing the Auckland border, we both received negative Covid-19 tests prior to undertaking the travel, and on our subsequent return to Auckland. We can also confirm we were not considered close contacts nor had we had visited any locations of interest.
"... We understand that strict compliance is required to stamp out Covid-19 from our country. We have let everyone down with our actions, and we wholeheartedly apologise."
Willis' mother - District Court Judge Mary-Beth Sharp - also released a statement, condemning the couple's actions.
"I am a District Court Judge, but I issue this statement in my personal capacity. Like the rest of New Zealand, I was appalled to learn of my son William and his partner's actions over the weekend.
"I was and am highly embarrassed. Had I known of their intentions ... I would have told them not to act so thoughtlessly and selfishly. I do not condone their conduct."
The couple have returned to Auckland, and police have not laid any charges.