The key point, which you have not mentioned, is where you will reside. Also relevant is whether the Irish company will have a place of business in the UK.
Thanks for the reply Padraig, I will continue to be a Northern Irish resident and the Irish company will have its registered office in ROI, no premises in the UK.
Your situation will be analogous to a resident of, say, Newry who commutes to a job in Dundalk. You are liable to tax in both jurisdictions, but eligible for Double Taxation Relief. I'm not up to date on how it works, and anyway most of it is sorted out in the background by the tax authorities: you just fill in the forms and let it happen.
There is some information here: [broken link removed]
With regard to your ROI company, where are the directors resident? Where is management and control of the company taking place? If it is in NI, the company could be dual resident (resident in ROI and NI) and be liable to Corporation tax in both countries with relief under the Double Taxation agreement.
Did you take advice before you set up the company?