 He was Chairman of the Newton Aycliffe and Peterlee New Town Development Corporation from 1971 to 1980.Stevenson was a non-executive Director of British Technology Group (1979–89), Tyne Tees Television (1982–87), Manpower Inc. (1988-2006), Thames Television (1991-93), J. Rothschild Assurance plc (1991–97), English Partnerships (1993-2004), BSkyB (1994-2001), Lazard Bros (1997-2002), St James's Place Capital (1997-2002), and Waterstones (2011-2016).He was Chairman of the National Association of Youth Clubs (1973-1981), Intermediate Technology Development Group (1983-1990), the Trustees of the Tate Gallery (1988-1998), Aerfi (formerly GPA, 1993-1999), Pearson (1997-2005), HBOS (formerly Halifax Plc, 1999-2008), the House of Lords Appointments Commission (2001-2008), and Aldeburgh Music (2002-2012).