Peyper rose through the ranks in South Africa, making his Super Rugby debut in 2008 while still in his 20s.
In 2011 he was named as an official for the 2011 IRB Junior World Championship in Italy, including the final between England and New Zealand where New Zealand won 33-22.
The following year, Peyper was promoted to the International Rugby Board's elite panel and was tasked with refereeing Scotland's 2012 tour of Oceania.
2015 saw him being selected as one of the twelve referees for the 2015 Rugby World Cup.
He was one of the 12 referees chosen to officiate at the 2019 World Cup as well, taking charge of the quarter-final between France and Wales.
