She replaces Mike Sheard, who has been in the role for 11 years and is retiring from the group at the end of July.
Trafford resigned from Lloyds in March after new CEO and former head of UK banking at Santander Antonio Horta-Osorio brought in Matthew Young, formerly comms director at Santander UK, as corporate affairs director.
Trafford, also a former group comms director at ITV, joined Lloyds in July 2010.
At ICAP, she will be responsible globally for all aspects of the firm’s comms, including investor relations, media relations, public affairs and customer and employee comms.
She takes up her new role on 11 July.
Michael Spencer, group chief executive officer, said that Trafford ‘brings a combination of a strong background and extensive international experience of corporate comms’.
Before joining Lloyds, Trafford ran her own consultancy and also worked for M:Communications. She was also head of communications at Dow Jones and Cable & Wireless Europe.
ICAP, headquartered in London and a member of the FTSE 100, is active in more than 32 countries and is the world’s largest interdealer broker.