Some policies require you to inform the insurer before you use the car abroad and Southern Ireland counts as abroad even though there are no borders. read your insurance policy details.
Any car insurance policy, taken out in any EU country, includes the minimum statutory third party cover of any other EU country.
So your policy ensures that you can drive within the law in Ireland (as well as in France, Germany, Spain, Lithuania, Greece, Finland, Hungary, Estonia, etc, etc).
However you'll need to read the actual policy details (or phone the insurer) to check whether any additional (non-statutory) cover, such as 'fully comp', applies in Ireland.
Before I emigrated to Ireland I went there every year on holiday to let her indoors see her family. I had to get a green card off my insurers to maintain my fully comp level of cover, otherwise I'd only be covered TPO. The various insurers I was with during this period never charged extra for it so it is worth making that call.