An "insurgent candidate" refers to a person running for office who challenges the established or mainstream political system. They often represent a new or different ideology and seek to bring about significant changes. Full definition
This means that the disruption to the political mainstream may not follow the antecedent of new parties but as insurgent candidates taking over established ones. (politicspolicymedia.com)
Bart Haggerty used Bloomberg's money to fund insurgent candidates against the Queens G.O.P. [David Seifman] (politico.com)
The Board of Elections chief investigator has filed a civil lawsuit against an obscure insurgent candidate in a special election last spring for an Assembly seat in Brooklyn. (wamc.org)