[citation needed] Before training to become a priest, in 1970 Moxon served a one-year term as a youth worker with Volunteer Service Abroad in Fiji, and then worked as a tutor in the Education Department at Massey University during 1974–75.

In 1987 Moxon was appointed Director of Theological Education by Extension for the Anglican Church in Aotearoa New Zealand and Polynesia, a position he held until 1993.

He was also an inaugural board member of the Ngati Haua Mahi trust, a work skills program for Maori in the Piako area from 2010 until 2013.

[13] In 1998 he joined the General Synod and bishops of the church in leading an ecumenical "Hikoi of Hope"[14] march from all over the country, which amounted to more than 30,000 people in Wellington, to present to the government the growing needs of unemployed and impoverished New Zealanders.

A wing of Bishop's Hall at Waikato Diocesan School for Girls and the residential age care building complex at Selwyn St Andrew's Village Cambridge, are named after him.

It was announced on 4 December 2012 that Moxon was to resign his Aotearoa New Zealand and Polynesia posts following his appointment as the Archbishop of Canterbury's Representative to the Holy See[16] and director of the Anglican Centre in Rome.

[10] Moxon was named an archbishop emeritus of the Anglican Church in Aotearoa New Zealand and Polynesia on 16 April 2013 by the General Synod / Te Hinota Whanui.

[19] Moxon and the Orthodox Archbishop Gennadios, representing their respective communions, supported Pope Francis in his ecumenical statements at St Paul's outside the walls in Rome.

Moxon completed his term of service in Rome by a private audience with Pope Francis on 16 June 2017,[21] and returned to New Zealand to retire.

In retirement Moxon has been made patron of the Faith Community Nurses Association;[22] He Pīhopa Āwhina (an honorary assistant bishop) in Te Manawa o Te Wheke since 2017;[7] a member of the Proprietor's board of Taranaki Diocesan School for Girls Stratford,[23] a member of the board of trustees and a Fellow of St Paul's Collegiate School Hamilton,[24] a Board of Governor's Fellow of College House Christchurch[25] and Priory Dean for Aotearoa New Zealand, of the Most Venerable Order of the Hospital of Saint John of Jerusalem (Order of St John).

Moxon is co-chair with Cardinal Tobin of New Jersey, of the Walking Together Foundation advisory committee, which seeks to fund Catholic and Anglican Bishop partnerships for aid, development, justice and peace globally.