They are the underwriters for 123.ie as far as I know. I was insured with them last year and luckily did not have to make a claim. I did however have to call their breakdown service on two separate occasions and I had the guy with me within 15 mins both times. Contrast that to my awful experiences with Axa in the past...and I'd take Travellers any day.
Didn't renew with them as AA got me a better deal but I'd go back.
Both myself and my partner are insured with them through 123.ie - used their breakdown assistance on one car and windscreen repair on the other with absolutely no issues at all.
Great to deal with - we saved nearly 300euro (joint) by switching to them.