He resigned at the beginning of June to focus on his marketing and communications agency Constratega, which he set up last year. Barnard had been in the CEA post for five years.
"I have really enjoyed my time at the CEA but I felt I couldn't do the job justice as well as build up my own business," he said.
There is no immediate replacement for Barnard, although there have been two board appointments: Sodexho Prestige sales and marketing director Alastair Scott and TM Group chairman Malcolm Williamson.
CEA chairman Sam Gill said: "We hope to have someone in the post by the end of the summer."