Are you doing your tax return on form 11?
In that case, even though the DIRT is already deducted at source, you still have to declare the deposit interest you received (before the deduction of DIRT). Then you will be charged 4% PRSI on that (assuming you don't have a PRSI exemption). If you're not filing form 11, but using something in "my account" (I think it might be form 12), then there shouldn't be any PRSI due. It hasn't been an issue for most people for many years as Irish deposit rates were essentially 0%. But now it is.
Note, the above is for Irish bank interest. I thought state savings interest was exempt from DIRT, and you didn't need to declare it in Form 11.