Administrator Zolfo Cooper has confirmed a large number of board members will also exit, including product development director Debbie Darlington and non-executive director Dave Hughes, the former chief marketing officer at Game.
Non-executive chairman Don Lewin will also depart, alongside group managing director Clinton Lewin and non-executive directors Hazel Cameron and Brian Jackson.
Clinton was put into administration by one of its suppliers, American Greetings, after it bought £35m of Clinton loans from two of Clinton's lenders.
The administrators revealed earlier in the week that store closures are expected as part of the administration.
The retailer has struggled to cope with the growing competition in the gift card market from the major supermarkets and the rise of online rivals such as Moonpig.
Moonpig is running a television campaign for its latest innovation, which allows the embedding of videos into cards through augmented reality technology.
Follow Matthew Chapman at @mattchapmanUK