Worries about free movement in the context of Brexit don't simply apply to people - concerns have also been raised about horses.
Agriculture Minister Michael Creed has warned the United Kingdom's exit from the EU has significant implications for Ireland's thoroughbred industry.
Horse racing and thoroughbred breeding essentially operates on an all-island basis, he said, with horses, trainers and riders regularly moving between both jurisdictions.
"The introduction of tariffs or regulations has the potential to increase the cost of business and reduce the free movement of labour and horses," Mr Creed said, in response to a parliamentary question from Independent TD Tommy Broughan.
Mr Creed said trainers in Northern Ireland are licensed by the Irish Turf Club, and races there are run under the Turf Club's Rules of Racing.
"Ninety per pent of runners at these fixtures are trained in the Republic with horses moving on a daily basis, so the return to a hard border would seriously disrupt this movement," he added.
"The two countries operate a single entity for stud book purposes. British and Irish foals are both registered in the one stud book, and together with France, have historically had a tripartite agreement between the respective Departments of Agriculture to facilitate free movement of thoroughbred horses."
Ireland's exports of thoroughbreds to Britain are worth around €225m each year. This may be at risk due to reduced trade flows following the Brexit vote, the Government believes. The horse industry overall contributes more than €1.1bn annually to the Irish economy.