Greig was a member of the New South Wales Police Force between 1979 and 2004 serving in both metropolitan and country locations. The majority of Grieg's service was operational in General Duties. He also had a number of years working in the Police Prosecuting Branch.
Greig commenced teaching at Charles Sturt University at the School of Policing Studies in 2008 as a lecturer on the Associate Degree in Policing Practice (ADPP) teaching in various policing subjects. He subsequently moved to a coordination and teaching role for a number of the Distance Educations subjects undertaken in year two of the ADPP. He is currently teaching on sessions one and two of the ADPP.
Greig has completed the Graduate Certificate in University Learning and Teaching (GCULT).