Clement spent his early years in the country's Wairarapa region, later studying drama and film at Victoria University of Wellington. His choice of college proved fortuitous, for it was there that he met two future collaborators who would change the course of his career: Taika Cohen and Bret McKenzie.

Joining Cohen as one-half of the sketch-comedy duo Humourbeasts, Clement went on to star with his partner in the quirky 2007 comedy Eagle vs. Shark (which Cohen also wrote and directed). With McKenzie, Clement formed the musical-comedy act Flight of the Conchords, an award-winning duo that ultimately won a Grammy, spawned an HBO series of the same name and earned Clement his first Emmy nomination.