On 25 May 2016, Murray was named in the 32-man Ireland squad to tour South Africa in a 3-test series. On 11 June 2016, Murray started in the first test against South Africa, scoring a try in Ireland's historic 26–20 win. On 26 October 2016, Murray was named in Ireland's squad for the 2016 end-of-year rugby union internationals. On 5 November 2016, Murray started in Ireland's test against New Zealand at Soldier Field, Chicago, scoring a try and a penalty in a 40–29 win that was Ireland's first ever against the All Blacks. On 23 January 2017, Murray was named in the Ireland squad for the opening two rounds of the 2017 Six Nations Championship. On 25 February 2017, Murray scored a try and earned the Man-of-the-Match award in Ireland's 19–9 win against France. Following his performances in the tournament, Murray was nominated for the 2017 RBS 6 Nations Player of the Championship award, alongside teammate CJ Stander.