[6] Carty made his first start for Connacht on 4 January 2014, when he played at fly-half against the reigning Pro12 and Amlin Cup champions Leinster, in another derby.

[8] The following season saw Carty continue to be first choice through to February 2016, when he injured himself on a water slide in Dubai and to have his spleen removed.

He returned to first-team action that April, but couldn't dislodge AJ MacGinty and Shane O'Leary and missed out on a place in the Pro12 Final on 28 May.

[6][8] The departure of MacGinty to Sale Sharks and injuries to new signing Marnitz Boshoff saw Carty return to first choice for the 2016–17 season.

[15] Carty also started the team's Champions Cup play-off with Northampton Saints at the end of the season.

[16] In December 2023 Carty earned his 200th cap for Connacht in 55–36losse to Saracens in the 2023–24 European Rugby Champions Cup.

[18] He made his debut on 24 February 2019, when he came on as a replacement in the 26–16 win against Italy in the Stadio Olimpico in Rome.