Three choices are to stay with your UK sim card and get charged at their "roaming" rates; get an "international sim" card that will cost something between normal and roaming rates in most countries or get local sim cards for UK & Ireland.
Something to be aware of is that most sim cards will stop working and any credit will be lost if they are not used for a couple of months or so. It may be necessary to replace the sim card for each visit.
I've noticed that O2 do an Ireland "bolt on" where you pay £1.99 and then pay their UK rates for calls while in Ireland (25p per minute!!). Other providers may offer something similar. You can browse some Irish sim cards on http://www.ebay.ie/sch/Sim-Cards-/29778/i.html