If you have CITIES paperwork for the tiger there is no issue. There are a few tigers in private hands in Ireland. I has an extensive collection of exotic animals and knows a good few in the trade.
I had a Garda ask me once at home if I had a licence for the iguanas. I was smart in answering him saying they only needed a licence if they wanted to drive or own a television.
The question I have to ask here is - why?
Why would a private individual want to own a tiger? Shouldnt a tiger be out in the wild doing what tigers do and interacting with other tigers? Is it not the height of cruelty to just keep one for pleasure? Or are they being kept for research and breeding purposes?