Clark, previously head of planning, and Simmons, former head of account management, will assist CHI chief executive Sarah Golding with the day-to-day running of the agency.
Last week Golding took on additional responsibility for the content division AllTogetherNow following the departure of Conor McNicholas.
Rebecca Munds takes on sole responsibility for running the planning department, reporting into chief strategy officer Neil Goodlad, while Charmaine Murray has been promoted to fill Simmons’ old role.
Golding said: "Not only do [Simmons and Clark] lead from the front as a brilliant account man and planner respectively, but they genuinely care about the work and the people here at CHI. They absolutely sum up the culture of this agency."
Clark joined CHI in 2002 from TBWA\London and has led the strategy on accounts including British Gas, Argos and Carphone Warehouse.
Simmons has worked at the agency since 2009, joining from Leo Burnett as a business director. He was promoted to head of account management in 2015.