Richard Barrett was born in Port Moresby, Papua New Guinea, but grew up in Darwin, Australia.
Richard attended the Australian Defence Force Academy and the Royal Military College Duntroon after finishing school. He graduated in 1995 and was allocated to the Infantry Corps. His first posting was to the 1st Battalion, the Royal Australian Regiment (1 RAR).
In 1999, Richard was posted as the Adjutant of the 11th/28th Battalion, the Royal Western Australia Regiment, and in 2000, he was posted to the 6th Battalion, the Royal Australian Regiment (6 RAR). During this period, 6 RAR deployed to East Timor, where Barrett served as the Battalion's Intelligence Officer.
On return to Australia, Richard was posted as a tactics instructor at the Royal Military College (RMC). In 2004, he returned to the Regiment as the Adjutant of the 2nd Battalion, was promoted to Major and served as the Officer Commanding Charlie Company.
In 2007, Richard attended Australian Command and Staff College. His thesis on civil-military operations was published by the Australian Army Journal as a working paper in 2010.
In 2008, Richard was posted as an exchange officer with the Marine Forces Pacific (MARFORPAC), Hawaii, where he was a lead planner for United States Marine Corps (USMC) international training activities throughout the Pacific region.
Richard deployed with the USMC to Afghanistan in 2009 as a part of the Marine Expeditionary Brigade, Afghanistan (MEB-A), as a G-3 Future Operations planner. In 2012, the MEB-A was awarded the US Presidential Unit Citation.
Richard was awarded the United States Meritorious Service Medal for his work with MARFORPAC and the Navy and Marine Corps Commendation Medal for his performance with the MEB-A.
Returning to Australia in January 2010, he was promoted the Chief Instructor of the Royal Military College of Australia (RMC-A).
At the end of his tenure at RMC-A, Richard deployed to the Headquarters of the International Stability Assistance Force Afghanistan (HQ ISAF), in the Future Plans cell. In 2012, he served as the Staff Officer (Policy) to the Chief of the Defence Force.
In 2015, Richard served as the Chief of Future Operations for Combined Joint Task Force Operation Inherent Resolve, which had command authority for all operations in Iraq and Syria countering the Islamic State.