Specht took up a position as Reader in plant ecology at the University of Melbourne in 1961, and became Acting Head of the Department of Botany in 1964. He moved to the University of Queensland in 1966 as Professor and Head of the Department of Botany and remained there until 1989. He was Visiting Professor in the Department of Forestry at the University of Oxford in 1970. He was Visiting Professor in the Department of Botany at the University of Leeds in 1975.