"Learairí" is indeed the plural of "learaire", which is a person who hangs around doing nothing, an idler, loafer or layabout.
If "Gael-linne" referred to the organisation that promotes the Irish language, I would expect the L to be capitalised. Instead, I suspect the author is making creative use of "Gael" to qualify "linn", which means a period of time. "Linn" is often used with a possessive adjective in phrases such as "lenár linn" = "in our day", "in our lifetime". The use of "Gael" with "linn" means that it is an authentically Irish period of time that is in question, but it's not so easy to come up with a good way to translate it into English while maintaining the idiom.
In case you're having trouble with the construction used here ("Tá sé ar..."), it means "He is one of the big loafers of our (Gaelic) day".