In my younger days I played clarinet (although not ITM), and now I play ITM on the wooden flute. I have also heard a few people attempt Irish trad tunes on the clarinet. My take on this is that the clarinet can be used to play Irish trad tunes that will sound Irish. Of course, to get the true Irish sound the player would need to use many of the ornamentation techniques that a wooden flute player would use, but since the clarinet is an open-holed instrument like the wooden flute most of these ornamentation techniques should be readily available.
The big issue in my mind would be keys. (That’s key signature of the tune, not the keys on the instrument.) The clarinet is what’s called a “transposing instrument”, which means that the note the player thinks they are sounding is not the actual note that sounds. In other words, if I’m playing a B flat clarinet, I look at the page, I see a C, I finger a C and play it, the note that comes out will be a B flat. On an A clarinet, the other common orchestral instrument, the player thinks they are playing a C, but an A comes out.
Given that, consider that most Irish tunes are in the keys of G, D, A and their associated minors. Thus to play these tunes and have them sound in their “correct” keys, the B flat clarinet player would have to play in A, E and B, respectively. These are not the best keys to play in on a clarinet, so playing these tunes would require a bit of skill on the part of the player. Likewise, to play in G, D and A on an A clarinet, the player would be playing in A# (B flat), F and C. These keys are not bad on the clarinet, but then again how many clarinet players actually have an A clarinet at hand? There are a lot more ex-band clarinet players around than ex-orchestra clarinet players, simply because bands use as many as 20 clarinets while orchestras use one or two. And band clarinets are all B flat instruments.
One place where the clarinet could work well would be on Irish tunes in keys like D minor and G minor. Fiddlers love these tunes, and on the B flat clarinet you’d end up playing them in E minor and A minor, which aren’t bad keys at all. Another aspect of the clarinet that would be nice on some Irish tunes is its low range. The clarinet goes down to G below the treble staff, which on a B flat clarinet is equivalent to the F just below the fiddler’s open G string. This would open up all those tunes that require fiddlers to use their G string. Flute players are stuck bumping notes up an octave in order to play those tunes, which sometimes sounds okay but other times doesn’t.
Still though, despite all this, I’d say clarinet has the potential to be at best a “niche” instrument in ITM. I would strongly recommend that a clarinet-playing ITM newbie pick up and learn another instrument such as whistle or flute first before attempting ITM on the clarinet.