Teina's father is best known from his show Pio!, The Life and Times of Te Tutu and his multiple TV appearances over the years.
In the weeks leading up to his death, Teina was full of hope on social media, looking forward to getting out of Starship Hospital and planning a trip to Fiji, writing on Instagram: "Can't wait for Fiji, thanks Pio".
He recently posted this video of Piha Beach which he captioned:
"These chemo drugs f*** with your head and really test your mental strength so it was good to be amongst nature before I'm locked up in a room for a while.
"I love the beach, I really feel I have a connection to the ocean...it makes me feel like I'm cleansing myself drawing out all the bad s***.
St Peter's College Principal James Bentley said the whole college is shocked and devastated.
Bentley said Teina had been with the school for seven years and was well known for being theatrical like his father.
"He's a great, fantastic kid. Very cheerful extremely well liked by staff and students. He had a great sense of humour.
"He's been an inspiration to us all with the battle he put up against leukemia.
Bentley said a testament to Teina's character was how he did some level two assessments last year from his bed at Starship Hospital.
"One of the really inspirational things is that even at Starship he continued with tutorial sessions. Lots of staff would go up there and take him through lessons. He was very keen to continue with his studies.
"He's very dedicated, he had big plans for his future."
The school held a mass today to remember Teina and will continue to support students with counselling.
Bentley said the Terei's were very involved in the school. Teina's older brother left the school in 2012 and their father was on the board of trustees. He said the Terei family, including his mother Deb and brothers Jack and Dalton were instrumental in setting up the school's kapahaka group in 2008.
"Their family has been really involved in the school."
St Peter's has 1350 students, 200 of which were in Teina's year 13.
Teina was with EMS Actor Management. His profile lists the teenager's skills as trampolining, swimming, bicycling, dancing, music and basic Maori.