Jeffery was born in 1937 in Wiluna, Western Australia, and he was educated at Cannington, East Victoria Park State Schools, and Kent Street High School. When he was 16 years old, he left Perth to go to the Royal Military College, which was Duntroon. After he graduated there in 1958, he went to Malaya in 1962 for a special service with the 2nd and 3rd Battalions of the Royal Australian Regiment. In 1965, he was seconded to go to the British SASR (Special Air Service Regiment) for a tour in Borneo. Then he returned to Australia as the leader of the SASR in Perth. From 1966 to 1969, he worked in Papua New Guinea with the 1st Battalion. He married Marlena Kerr, who lived in Sydney during this work. After that, in 1972, he was chosen to go to the British Army Staff College at Camberley. Then he was chosen as the person to help with the 2nd Battalion in Wewak PNG. In 1976, he became the commander of the SASR and was appointed as the member of the order in Australia. He was also chosen to attend the Royal College of Defence Studies in London in 1985.