Greaves' grandfather, Walter Baddeley, was Bishop of Melanesia, based in the Solomon Islands, during World War II.
Following his ordination he served in a number of roles including in Ceduna in South Australia and Katherine in the Northern Territory,[2] as Dean of Christ Church Cathedral, Darwin from 2007 to 2013,[1] and immediately prior to his appointment as Bishop for the Northern Region in the Diocese of Brisbane, as rector of St Mark's Anglican Church in Buderim and Archdeacon of the Sunshine Coast.
[2] On 1 September 2023, Greaves was elected as the tenth Archbishop of Brisbane and was installed in the position on 16 December 2023.
On his appointment, Greaves said that he was looking forward to serving with the diocesan community as it discerned where the Spirit was leading it, and advocating in important justice spaces.
[8] In 2010, he told ABC Radio National that he would be "happy to abandon" the Apostles' Creed.