On 23 October 2009, Archer made his Munster debut as a replacement against Edinburgh during a Celtic League fixture. He was part of the historic Munster team that beat Australia 15–6 at Thomond Park on 16 November 2010. He made his Heineken Cup debut as a replacement in Munster's Round 5 26–10 win against Castres on 14 January 2012, during the 2011–12 Heineken Cup. Archer was part of the team that defeated newly crowned Heineken Cup champions, and arch-rivals, Leinster 19–9 in the 2011 Magners League Grand Final on 28 May 2011. With Munster A, Archer won the 2011–12 British and Irish Cup. He scored his first try for Munster in a 2011–12 Pro12 league fixture against Ulster on 5 May 2012. He signed a two-year contract extension with Munster in January 2013. In October 2015, Archer was ruled out for a number of months after sustaining a neck injury that required surgery. Archer made his 150th appearance for Munster on 1 January 2018, doing so when he came off the bench against Ulster in a 2017–18 Pro14 fixture. He signed a two-year contract extension with Munster in January 2018. Archer made his 150th Pro14 appearance in Munster's 37–28 win against Italian side Benetton in round 20 of the 2018–19 season on 12 April 2019. He won his 200th cap for Munster in their 2019–20 Pro14 round 7 fixture against Edinburgh on 29 November 2019, becoming the eleventh player to achieve the accolade for the province. Archer signed a two-year contract extension with Munster in January 2020, a deal that will see him remain with the province until at least June 2022.
Archer has represented Ireland at underage levels up to Under-20. He received his first senior call-up when he was selected in the Ireland Wolfhounds squad for their game against England Saxons in January 2012. He went on to make his Wolfhounds debut against England Saxons on 28 January 2012. He was selected on the bench for Ireland's 2013 Six Nations Championship game against France on 9 March 2013, his first senior call-up, though he did not come on during the 13–13 draw. Archer made his senior debut for Ireland a week later, coming off the bench against Italy. On 23 October 2013, Archer was named in the Ireland squad for the 2013 Autumn Tests. He came off the bench against Australia on 16 November 2013 to win his second, and, so far, last, cap. Archer came off the bench for Ireland Wolfhounds against England Saxons on 25 January 2014. He was named in the Ireland squad for the 2014 Guinness Series on 21 October 2014. Archer was named in the Emerging Ireland squad for the 2015 World Rugby Tbilisi Cup on 19 May 2015. He started in the opening 25–0 win against Emerging Italy on 13 June 2015. Archer started in the 33–7 win against Uruguay on 17 June 2015. He also started in the 45–12 win against Georgia on 21 June 2015, a win which secured the tournament for Emerging Ireland.
