He joined the RAAF through the Australian Defence Force Academy in 1993 and gained his pilot's wings in 1998.

[8] According to his father, Chappell's interest in aviation was sparked by seeing the film Top Gun as a child.

[10][12] He was one of the first Australians to fly on operations over Iraq, piloting an F/A-18 Hornet as escort to tanker, early-warning and control aircraft.

[10][12] Selected for an exchange posting with the United States Air Force, Chappell served as the Assistant Director of Operations for the recently reactivated 65th Aggressor Squadron, based at Nellis Air Force Base in Nevada, from July 2005 to December 2007.

He was subsequently awarded the United States Meritorious Service Medal for the "exceptional initiative and vision" he demonstrated in his work with the squadron.

[15] Chappell graduated from the Australian Command and Staff College with a Master of Military and Strategic Studies in 2013.

[10] In January 2017, as part of the Australia Day Honours, he was awarded the Conspicuous Service Cross for "outstanding achievement in air combat development and preparedness" as commander of No.

He was promoted to air vice-marshal and appointed Head Military Strategic Commitments in July 2022.

[10] In April 2024 the Minister of Defence, Richard Marles, announced that Chappell will be appointed Chief of Air Force in July 2024.