He was then consul in Hong Kong in 1964, press counsellor in London in 1967 and trade counsellor there in 1971. Ternström was deputy head of the Administration Department at the Foreign Ministry in 1973. He was ambassador in Tunis in 1976 and served in the Swedish UN delegation in New York City in 1978. Ternström was ambassador in Cairo and in Khartoum from 1981 to 1986. In 1981, while Ternström was ambassador in Egypt, he escaped unhurt after the Egyptian President Anwar Sadat was assassinated. He ended his diplomatic career by being ambassador in Bangkok from 1986 to 1992.