The negotiations and partition of Ireland and the establishment of Northern Ireland as a self-governing province (rather than being governed from Britain):
https://en.wikipedia.org/wiki/Partition_of_Ireland
And then the Troubles, which were a sectarian conflict between Catholics and Protestants within Northern Ireland itself, that stemmed from Protestant oppression of Catholic rights protests (patterned after the US civil rights movement). The Wikipedia pages are really good, but the top level page is great because it covers the early days so well:
Northern Ireland receives heavy subsidies from the UK government. I imagine the UK would be quite happy to cede it to the Republic of Ireland were this politically feasible and not likely to kick off another round of sectarian violence. Ireland may want the six counties in principle, but might be a little unhappy with the bill.