McNeill will depart the Omnicom-owned shop at the end of the year to work on "new challenges".
She was most recently the agency's chief executive, having previously worked as its managing director.
Matt Kwiecinski, the managing director of Agency Republic, will continue to lead its senior team, which also includes the planning director, Alistair Millen, and the executive creative director, Al Campbell, who returned earlier this year from WCRS.
They will work closely with Andy Hobsbawm, the former European chief of Agency.com, who chairs the agency's executive advisory board.
Agency Republic lost its flagship O2 digital account after a pitch last year but has since secured new-business wins including Shape, Nivea, Vodafone and Cancer Research UK.