Yes you register with the IAA (Irish Aviation authority) It's 5 Euro and you get a little sticker to put on your drone, it comes in the mail so do it long before you plan to go. I have TSA pre check so I didn't have to remove my drone departing the US. I did however have to remove my Drone at Shannon airport departing Ireland. They basically looked at it asked me a few questions and let me on my way.
Basically the airspace in Ireland is open except around the "Major:" Airports (5 miles) Shannon Dublin Cork Kerry and Donegal. There is also a no fly zone around the Aran Islands. There is a map of the airspace available online.
As well, the Office of Public Works (OPW) has said Drones are not allowed in there airspace. My understanding is as long as you take off from non OPW property they do not own the airspace above the IAA does. There is a no Drone sign at the Cliffs of Moher. Again my understanding is that you can not take off from the visitor center but you can fly off property. There is a trail that follows the Atlantic from Hags head to the visitor center. You can fly and take off from this trail. Don't take off from the parking lot as you will be asked to leave. You have to be mindful of the crowds at the Cliffs. It's a major tourist attraction that was busy even in December when I went. It was busy in April when I went. It's basically busy year round. You really need to be careful as I think the biggest complaint people have in Ireland is flying drones over people.
Be respectful, don't fly over crowds. Try and find a out of the way place to launch get your shots and move on. I didn't feel comfortable flying at a few of the more notable castles like Trim and Cashel. The crowds were heavy (even in December) and I felt the risk just wasn't worth it. I do have to tell you it was nice having a small drone. The
M2P is quiet and on most shots no one even knew there was a drone orbiting them.
Also a word on the Guardai (the police) you're lucky to even see one especially in Rural Ireland. Fly safe and you should be fine.