I'm not quite sure that 3 is the Illustrious Order of Te Arikinui Queen Te Atairangikaahu. I have a feeling it is The Order of King Potatau Te Wherowhero, single class exclusively awarded to Reigning Sovereigns. Correct me if I'm wrong, apologies if I am. Were you able to confirm the honours and insignia, if so, where did you received this information?
Kiingi Tuheitia commissioned a companion book to the Orders to explain more on their purpose and potential recipients.
However, this is yet to be released to the general public. Nor have there been any public investitures with a list of recipients including why they received their respective honour. Hopefully this system is made more open with more detailed information forthcoming sooner rather than later.
I believe Kiingi Tuheitia is wearing the Insignia of the Order of King Potatau Te Wherowhero. I can't quite work out all the breast stars, therefore I'm not sure if Kiingi Tuheitia is wearing all 3 of his honours or others he has received. Makau Ariki Te Atawhai (Consort to the King) is wearing insignia of an honour as well.