Medley, who started in the role this week, replaces Tessa Willmott, who has stepping down after more than six years at Wild Card.
She left the business to pursue other opportunities, Medley said.
Agency founder Kate Wild added: "Whilst of course we are sad to say goodbye to Tess and thank her for her contribution, we are much looking forward to drawing on Richard's skills and experience."
Medley, who will lead a team of 20, has been tasked with growing the agency and developing "new, complimentary offers", he said.
"We are renowned for [our work in] food, drink, lifestyle, travel and design/interiors. That will stay the case, but I will also be exploring other sectors where our experience might translate well," Medley said.
Prior to spending a year with Frank before departing to pursue "different-shaped roles", Medley was MD at Nexus Communications between 2012 and 2015, and before this he was MD at corporate consultancy Spider PR. He was also MD at Publicis Consultants from 2007 to 2010.
Wild Card, whose clients include Highland Spring, Tetley and Lurpak, also has divisions in Bristol and Truro, known as Wild West.