Air New Zealand has flights between Tongatapu and Auckland daily except Sunday, with connections in Auckland to/from Brisbane, London, Los Angeles, Melbourne, Sydney, and many other destinations.
Virgin Australia, part of the Virgin group, operates direct no frill flights to Tongatapu from Auckland or Sydney four times week.
The Fijian airline, Fiji Airways, has service to Tongatapu from Nadi or Suva four times a week except Sunday with connections to/from Los Angeles from Nadi.
Around Christmas and the Heilala Festival July 4, all flights are fully booked by Tongans returning home.
Be sure to reconfirm your onward flight reservations.