Carter was born in Tamworth, Australia, and represented Sydney University before signing his first professional rugby contract with the ACT Brumbies in 2010.

He made his Super Rugby debut in 2011 and went on to make more than 120 appearances for the Canberra-based side during the next nine seasons, including the last two as captain.

In 2014, Carter made his Test debut for the Wallabies and joined a unique group of father and sons to have represented the Australian national rugby union side.

He moved to Ulster ahead of the 2019/20 northern hemisphere season and, has since, made 58 appearances for the Irish club including captaining the Belfast-based side.