[3] He made his competitive debut for the senior Munster team on 21 September 2018, aged 19, coming off the bench to replace Mike Sherry in the provinces 2018–19 Pro14 fixture against Cardiff Blues.
[4][5] He scored his first try for the province in their 39–9 win against Welsh side Dragons on 28 September 2019, in Munster's opening 2019–20 Pro14 fixture.
[6] Barron was promoted from Munster's academy to their senior squad ahead of the 2020–21 season,[7] and made his first start for the province in their 31–17 win against Italian side Benetton in round 16 of the 2020–21 Pro14 on 19 March 2021.
[8] Barron signed a one-year contract extension with Munster in March 2021,[9] and made his Champions Cup debut for Munster in their 2021–22 pool B round 2 fixture at home to French club Castres on 18 December 2021, coming on as a replacement for Niall Scannell in the province's 19–13 win.
[1] Barron was selected in the Emerging Ireland squad that travelled to South Africa to participate in the Toyota Challenge against Currie Cup teams Free State Cheetahs, Griquas and Pumas in September–October 2022.