Greive joined the Australian Army after leaving high school and underwent training at the Royal Military College Duntroon in Canberra. Whilst an undergraduate at RMC Duntroon, Greive undertook a military exchange with the Royal Thai Military Academy, during which he toured Thai/Cambodian border military installations and refugee camps. Upon graduation as a commissioned officer (Lieutenant) Greive was posted to the 3rd Battalion of the Royal Australian Regiment (Para), and assumed command of 1st Platoon, Alpha Company – a paratroop combat rifle platoon. Greive's specialist combat qualifications include: Airborne Operations, Air Mobile Operations, Survival, Mine Warfare & Anti Handling Devices (Instructor), Heavy Weapons – Direct Fire Weapons, Anti-Armour, Heavy Machine Guns (Instructor). He continued to serve in this capacity until 1993, when he left the military due to a tropical respiratory infection that led to asthma.