Murray received a BA degree from Trinity College Dublin and completed an LLM at the University of Cambridge.

[5] He represented the State in 2005 in defending a judicial review case taken by the former judge Brian Curtin.

[6] He has also appeared for the State and the Data Protection Commissioner in defending actions launched by Max Schrems,[7][8] the Office of the Director of Corporate Enforcement in a case against Independent News & Media and the Irish Bank Resolution Corporation against members of the Seán Quinn family.

[11] He has acted for the State in a first instance hearing taken by Graham Dwyer, the man convicted of the murder of Elaine O'Hara, in the High Court, regarding the applicability of the Data Retention Directive in Irish law.

[4] He provided advice on the law of abortion at a meeting of the Citizens' Assembly in March 2017, which made recommendations which ultimately resulted in the Thirty-sixth Amendment of the Constitution of Ireland.