Chinn was educated at Clifton College and King's College, Cambridge and started his career at Lex Garages (later Lex Service plc) where he followed in his father Rosser's footsteps, ascending to the role of Managing Director in 1968 at the age of 33 and to Chairman and Chief Executive in 1973. In 1968 Lex made £1m in profits, but by the time he retired in 2003 the profits were over £85m. His most notable achievement at Lex was the acquisition of the RAC in 1999 for £425m, which completely changed the nature of the company and led to its change of name in 2001 to RAC plc. In 1989 he initiated the Lex Report on Motoring (now the RAC Report on Motoring), the most authoritative study of motorists' attitudes in Britain.
He has become a successful entrepreneur. He is Senior Adviser, CVC Capital Partners; Chairman of ITIS plc, a traffic information company; Chairman of Streetcar (carsharing), the largest UK pay-as-you-go car club, concentrating its operations around London and 5 other UK cities; Chairman of the Mayor's Fund for London and Chair of the government's Motorists` Forum.
Chinn's leadership roles include Chief Barker of the Variety Club of Great Britain for 2 successive terms (1977 and 1978), Chairman of the Friends of the Duke of Edinburgh's Award Scheme (for which he received his CVO in 1989), Vice Chairman of the Wishing Well Appeal for Great Ormond Street Hospital (for which he received his knighthood in 1990), Deputy Chairman of the Royal Academy Trust.
Throughout his life he has also devoted himself to the Jewish Community in Britain and supporting the State of Israel. His roles in Jewish communal life have included Chairman (and now President) of the Joint Israel Appeal, the leading organisation in Britain supporting Israel's humanitarian needs; board member of The Jewish Community Centre for London, President of Norwood from 1996 to 2006; one of the founders of the Jewish Association for Business Ethics (and now Vice President). Sir Trevor currently sits on the Executive Committee of the Jewish Leadership Council and Chair of London Mayor's Fund.