Jeffery Kissoon was born in Trinidad and came to the UK at the age of 10. He originally trained as a drama teacher at the Coventry College of Education (subsumed into the University of Warwick in 1978 and also known as Canley College). He subsequently worked at St Peter and St Paul's Primary school in Coventry. In an interview with the Coventry Evening Telegraph, he also stated that he got his "first taste of acting back in 1964 when I was about 15 and at school in London"
("'Sir' puts on a great act following his instincts", Coventry Evening Telegraph, 28 July 1993).

"The first ever Associate Artist has been appointed to Birmingham Repertory Theatre. Jeffery Kissoon, who starred as Othello in the theatre's recent production, is director Bill Alexander's choice for the Honour. The new appointment follows the pattern of other major companies, such as the Royal Shakespeare Company and the Royal National Thatre, in honouring members of the profession. Mr Kissoon – soon to appear in Julius Caesar for the RSC at Stratford – said: 'I'm honoured, flattered and surprised to have been offered this prestigious appointment.'" ("Curtain Calls", Birmingham Evening Mail, 2 July 1993)

Kissoon's other classical credits include playing Tamburlaine at the Glasgow Citizens, which also played at the Edinburgh Festival. He also toured nationally with Janet Suzman in a revival of The Duchess of Malfi. At the Birmingham Rep, Kissoon played Fainall in William Congreve's The Way of the World in Bill Alexander's 1995 production.