I probably first consciously heard "The Hills of Connemara" on a Clancy Brothers record but the version I sing is from Soodlum's 100 Irish Ballads Volume 2
who describe it as a song about the production of illicit alcohol (poteen) and the attempt by the Excise Officers to control it. I especially like the verse
A gallon for the butcher, a quart for Tom,
A bottle for poor old father Tom,
To help the poor old dear along;
In the hills of Connemara."