https://ec.europa.eu/info/business-economy-euro/euro-area/enlargement-euro-area/who-can-join-and-when_en
National target dates for adoption of the euro
"The Treaty does not specify a particular timetable for joining the euro area, but leaves it to Member States to develop their own strategies for meeting the condition for euro adoption. Seven of the 13 Member States who joined the EU since 2004 have already joined the euro area, most recently Lithuania on 1 January 2015."
States need to agree to adopt the Euro but as there is no deadline for doing so, that is not a huge issue.
What are the border controls between Ulster and the ROI? The same arrangement could apply to Scotland.