Under the terms of the Chicago Convention on International Civil Aviation, Ireland and the other contracting states have agreed to, in general, allow aircraft registered in each others' countries to overfly their territories.
There is no international statutory requirement on private owners to insure against liability for loss or damage arising from the operation of their aircraft. While individual countries may impose such obligations, it is understood that very few do so.
In the case of commercial aircraft, owners' or operators' liability for loss or damage to passengers arising from the operation of their aircraft is generally covered as part of the conditions under which they are granted authorisations to operate.