Born and raised in Auckland, New Zealand, Abercrombie attended Westlake Boys High School and played four years of school basketball. In 2005, he captained the basketball team to the title at the Secondary School National Championships. That year, he also served as the school's deputy head boy and was captain of the volleyball team. As a junior, Abercrombie played for the North Harbour Basketball Association and represented New Zealand with the Junior Tall Blacks. In November 2005, Abercrombie accepted a scholarship deal with Washington State University. He spent two seasons with the Cougars, redshirting his freshman season in 2006–07 before seeing action in 12 games in 2007–08.
Professional career
New Zealand Breakers
After returning home following his college stint, Abercrombie joined the New Zealand Breakers in the Australian NBL as a development player for the 2008–09 season. He played 13 games in his first season with the Breakers, and was elevated to the full squad for the 2009–10 season. He missed four games in the back half of the season with an ankle injury. In the 2010–11 season, Abercrombie helped the Breakers reach their first ever grand final series, where they defeated the Cairns Taipans 2–1 to win their maiden NBL championship. He was subsequently named the Grand Final MVP. Abercrombie went on to win three more championships with the Breakers in 2012, 2013 and 2015. Abercrombie played his 250th NBL game in October 2017, and his 300th game in February 2019. In October 2019, Abercrombie committed to the Breakers until the end of the 2021–22 season. In 2019–20, Abercrombie became the second player in NBL history to join the exclusive 50–40–90 club. Abercrombie averaged 12.1 points per game for the season while shooting 50.0 percent from the field, 46.5 percent from three-point range and 90.5 percent from the free throw line.
New Zealand NBL
In 2009, Abercrombie debuted in the New Zealand NBL with the Waikato Pistons. He helped the Pistons win the championship while claiming Rookie of the Year and All-Star Five honours. He continued on with the Pistons in 2010 and earned All-Star Five honours again while helping the Pistons make a second consecutive grand final appearance. He returned to the Pistons for a third season in 2011 and once again earned All-Star Five honours. In 2019, Abercrombie played half a season with the Wellington Saints and helped them win a championship while claiming Grand Final MVP honours.
Abercrombie made his debut for the Tall Blacks in 2006. In 2007, he represented New Zealand at the World University Games. He has been a regular with the Tall Blacks since 2009. In 2018, he won a bronze medal at the Commonwealth Games. In 2019, he played at the FIBA World Cup.
Personal
Abercrombie is the son of Colin and Judy. He is the oldest of three children, with brother Hayden and sister Nicola. Abercrombie and his wife Monique have two children. Abercrombie studied a Bachelor of Science at Massey University.