The giant of Irish country music is Bap Kennedy. "Domestic Blues" is his most important album, so you may consider listening to his songs.
Cara Dillon is also a talented female country singer. Many songs such as "Craigie Hill" are very good. You can listen to them on QQ Music.
Altan's "Daily Growing" is a song with a story. Altan was the most outstanding traditional Irish folk band in the 1990s.
However, in current Irish music, the Kerr Family Choir is performing better. Although their songs are modern, they have strong traditional elements in them, so you can also Go and try to listen.
These are all recommended by others, you might as well listen to them!