Even as a junior, Coetzee stood out as the fastest bowler among his peers. South Africa picked him for their U-19 side when he was only 16. At the 2018 U-19 World Cup he took 8 wickets in 4 matches, including a five-wicket haul against New Zealand. Later in 2018 he debuted in List-A and T20 cricket for Free State. His First Class debut came in 2019 for the Knights, skipping the second-tier provincial system entirely. In 2020 he appeared at a second U-19 World Cup.
Franchise interest arrived soon afterwards. In 2021 the Rajasthan Royals brought him in to replace the injured Liam Livingstone. He later played for the Texas Super Kings in the first season of the MLC.
His first national call-up came in 2022, for South Africa's tours of England and Ireland, and he was also part of the squad for the 2022 T20 World Cup. He did not make his international debut until February 2023, when he received a Test cap on a tour of the West Indies. Caps in ODIs and T20Is came next, and Coetzee, recognisable by his headband, became part of a strong group of four South African pace bowlers. In 2023 he was selected in South Africa's 15-man squad for the Cricket World Cup.
As is common for tall fast bowlers, Coetzee has already dealt with a number of injuries, and keeping him fit is a key concern for Cricket South Africa.