THERE ARE CURRENTLY NO SERVICES
Jetstar, which used to fly in competition with Air New Zealand before the pandemic says it can't restart operations because Australia is not going to be in the "bubble" (but see above for plans to operate out of New Zealand)
Prior to lockdown, Air New Zealand operated a direct flight from Sydney to Rarotonga. It departed Sydney at 9:15 pm on Friday crossing the international dateline and arriving in Rarotonga at 6.25 am on the same day. The return flight left on Thursday at 3.15 pm arriving in Sydney at 7.20 pm on Friday. The journey time is around 7 hours. As this flight was heavily subsidised by the Cook Islands government, its future could be in doubt. It can't operate at all right now because the USA is not in a travel bubble with the Islands. Virgin Australia, which also used to have direct flights has ceased operations completely.