On Tuesday 2 May 2017 the Irish Government published a broad ranging position paper on Brexit entitled "Ireland and the negotiations on the UK's withdrawal from the European Union – The Government's Approach".
Whilst this position paper does not provide an in-depth discussion specifically on data protection it does provide some high level insights into the Government's initial thoughts on how Brexit will affect data protection regulation.
The position paper recognises some fundamental Brexit related points in so far as data protection is concerned including that the "UK may no longer be bound by EU law nor within the direct jurisdiction of the EU Court of Justice once it withdraws from the EU." and that "a solution will need to be found in the context of any future relationship agreement […] to how the UK could meet the EU standards with regard to data protection .."
The paper states that "this is of particular importance for Ireland in the context of co-operation against organised crime and terrorism, and in the maintenance of the sharing of information which is an essential aspect of the Common Travel Area".
The UK's ability to obtain a favourable "Adequacy" decision from the European Commission or a bi-lateral agreement as part of its "future relationship agreement" with the EU will also be a priority for the UK government. This is likely, however, to bring the UK's proposed decision (as mentioned in its recent White Paper on the proposed Great Repeal Bill) to exclude the Charter of Fundamental Rights of the EU - and its domestic surveillance laws - sharply into focus.
See here for the full position paper.