On 23 February 2016, she jumped 4.71 m (15 ft 5 ⁄4 in) at the Vertical Pursuit international pole vault competition at Millennium Institute of Sport in Auckland, setting four new records: New Zealand national, New Zealand under 20, New Zealand resident, and New Zealand all comers. She was subsequently added to the New Zealand team to the 2016 IAAF World Indoor Championships
On 5 March 2016, she jumped 4.80 m (15 ft 8 ⁄4 in) at the national championships in Dunedin, to surpass her own New Zealand record. It is not clear whether or not this set a new Oceania record. The IAAF normally requires a minimum of three competitors in an event for a record to be ratified and in this case, there were only two. Regardless, the Oceanian record was broken later in July 2016 by Alana Boyd of Australia, with a jump of 4.81 m.
In April 2016, McCartney was selected to compete at the 2016 Summer Olympics in Rio de Janeiro. In the Olympic final, she cleared 4.50 m, 4.60 m, 4.70 m, and her personal best 4.80 m on her first attempts, but was eliminated after failing to clear 4.85 m. Her 4.80 m result and no misses up to that height saw her place ahead of Australia's Alana Boyd to win the bronze medal. At age 19 years and 252 days, McCartney became the youngest Olympic medallist in the women's pole vault. She was also only the fourth New Zealand Olympic medallist in a field event, after Yvette Williams (long jump, 1952), Valerie Adams (shot put, 2008, 2012, 2016), and Tomas Walsh (shot put, 2016). BMX rider Sarah Walker, an Olympic silver medallist, approached McCartney at the Halberg Awards ceremony on 18 February 2016 and has been mentoring her since.
McCartney won the Emerging Talent category of New Zealand's Halberg Awards for 2015 at an awards ceremony held on 18 February 2016. The year before, she was a finalist in the Halberg Awards Emerging Talent category, which was won by cyclist Regan Gough.
In October 2016, McCartney became an ambassador for Beef and Lamb New Zealand, joining existing athlete ambassadors Lisa Carrington, Sophie Pascoe, and Sarah Walker.
Also in October 2016, McCartney became a brand ambassador for Blueberries NZ.
In December 2016, McCartney featured alongside several other notable New Zealanders in an aircraft safety video for Air New Zealand, entitled Summer of Safety.