Meredith replaces Ben Stephens who is leaving to relaunch the mail-order company Roxtons.
She will initially combine her new role with that of head of planning while Rapier searches for a successor. Meredith joined the agency in September 2002. She previously headed the planning department at Proximity London.
In the past two years, Rapier has attempted to build its planning resource by hiring from a variety of backgrounds including ad agencies, management consultancies and data companies. Meredith is credited with pulling this expertise together and organising it around clients.
Jonathan Stead, Rapier's chief executive, said: "Ally's planning background, together with her drive and ambition for the agency, makes her ideal for the role."
Meredith, alongside Stead and the creative director John Townshend, completes the agency's senior management team.
Additionally, Rapier has made two other hirings. Justine Parkinson, a senior planner, and David Parslow, a client director, both join from Proximity.
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