I think OTT is the only major promotion in Ireland, that runs shows on a consistent basis. You would see other smaller promotions throughout the RoI and NI run shows but very sporadically.
I can't really say much for the South, but in Northern Ireland, we have Titanic Wrestling which used to be Pro Wrestling Ulster (and Ulster Championship Wrestling before that), and Wresolution that run shows in Belfast. While Wrestling Ireland runs shows out in the southeast of the country.