A long document but starts to deal with the issue.
The Impact and Consequences of Brexit for Northern Ireland
"During the 2016 UK EU referendum campaign, the future UK Prime Minister, Theresa May, asked: ‘if the UK pulled out of the EU and came out of free movement, then how could you have a situation where there was an open border with a country that was in the EU and had access to free movement?’ Since then, the UK government has been more emollient in terms of what is envisaged regarding visible partition. In the UK Government’s Brexit White Paper, the maintenance of the Common Travel Area between the UK and Ireland
was listed as one of the twelve negotiating priorities.
However, regular assurances of ‘no return to the borders of the past’ have not been accompanied by clarity over what is proposed. Moreover, the ‘borders of the past’ have changed largely due to the improved security situation. There is no demand for control of the movement of people across the border from any political parties in the Northern Ireland Assembly.
Up to 30,000 workers are ‘cross-border’ in that they live and work on different sides of the Northern Ireland/Republic of Ireland border and would be directly inconvenienced by border checks. Seven per cent of Northern Ireland’s employees are drawn from the European Economic Area, a figure exceeded in the UK only in London. In the event of a lack of control of movement across the border, EU immigrants in search of UK work could enter the UK across the border unchallenged. They could reside in Northern Ireland or across the Irish Sea in Great Britain. The immigration policing operation, Operation Gull, currently monitors non-EU illegal immigration into Britain via Northern Ireland. This could be extended to deal with immigration from EU countries but would require additional resources.
Immigration policy for Northern Ireland is not a matter for the Northern Ireland Assembly. It is a power reserved for Westminster. If the UK government devolved this power to the Assembly, it would allow local control over entry into Northern Ireland and maintain a ‘soft’ border, but there is zero prospect of such devolution.
UK immigration policy may become a de facto British immigration policy, in that controls are maintained at mainland ports rather than at UK’s only land frontier. In effect, there would be no control of cross-border movement on the island of Ireland and the UK could conceivably confine its border control frontier to England, Scotland and Wales. This would potentially place Northern Ireland within a more overtly ‘Irish context’, a feature which would be welcomed by nationalists but might concern some unionists.
UK immigration controls could be shifted towards Irish ports and airports in the same way that immigration clearance for entry into the United States is undertaken at Dublin Airport. The Ulster Unionist Party has suggested that ‘imaginative new arrangements could draw on the experience of the Republic surrendering sovereignty at Dublin Airport to the United States for customs and security clearance, and the Calais model where HM Government part funds the arrangement in France’.
However, the existence of a similar facility for the UK in Ireland would be much more politically sensitive given the historical context. As such, this policy option of a shift in the location of controls may not be feasible".
Highly unlike that the Irish republic will put extra check on EU citizens, so they would be free to come to Ireland and move wherever they chose. However, the UK government has said the Common Travel Area is up for negotiation which means a border in the island of Ireland could lead to a Calais situation on the border. Or of no border, the north would act as a holding area for EU citizens if they chose to go north - something the DUP don't want.
There will also have to be alterations to the Good Friday Agreement.
