Estcourt was educated at New Town High School and Elizabeth Matriculation College and graduated with a Bachelor of Laws degree with Honours from the University of Tasmania in 1974.

[2] In 2001 Estcourt was appointed part-time Deputy President of the Commonwealth Administrative Appeals Tribunal and sat all over Australia hearing chiefly visa refusal and deportation cases.

[12] These also included a rarely permitted intervention in the High Court of Australia on behalf of the UNHCR as amicus curiae in Minister for Immigration v QAAH.

[13] In 2009 he was engaged pro bono from Melbourne as senior counsel in litigation against the Tasmanian Government over conditions in the Behavioural Management Unit in Tasmania's Risdon Prison.

Estcourt's involvement in that trial led to an allegation that he had entered into an illegal bargain with the Tasmanian Government to be appointed the Solicitor General for Tasmania in exchange for acting for Green without fee.

[25] In the Australian Queen's Birthday Honours in 2018, it was announced that Estcourt had been made a member of the Order of Australia for "significant service to the judiciary as a Judge of the Supreme Court of Tasmania, to legal education, and to professional law societies".