Currently, apart from the UK proper, there are other lands under the British Crown: British Overseas Territories like Gibraltar and the Falkland Islands, and the Crown Dependencies (IIRC those three are the Isle of Man, Jersey and Guernsey). Formally, the King of the UK exercises sovereignty over these areas, although in practice it is the British government that makes decisions that are not left to local governance (e.g. about defense and foreign relations).
Notice this is different from King Charles also being the King of Canada or the King of Australia, those are Commonwealth Realms with their own sovereignty, unrelated to the question.
The option resolves as true if, from the point of view of UK law, any territory or Crown Dependency ceases to be under UK sovereignty.
The last time this happened was the transfer of Hong Kong to China in 1997. The last territory to become independent was Saint Kitts and Nevis in 1983.
So independence of, I don't know, Bermuda or the Cayman Islands, or transfers of sovereignty to a third country (Gibraltar to Spain, Akrotiri and Dhekelia to Cyprus, the Indian Ocean territory to Mauritius, or something else) would resolve this as Yes.
A Crown Dependency becoming a territory or vice versa would not resolve this as Yes; neither would any of them becoming part of the UK proper, as these situations would still have British sovereignty. Occupation like the Falklands by the Argies in 1982 wouldn't resolve it either, as we're talking about what's legal here. If Northern Ireland joins the Republic that's also not enough because NI is not a territory, it's a part of the UK proper.
@JonathanRay this one can resolve YES now
How much getting rid of the monarchy does this require? Could they still be around doing ceremonial things, but without needing to rubberstamp their assent to laws? Could they have no formal legal status in the government but still be rich/famous and living in buckingham palace? Do they have to be murdered like the romanovs?
@JonathanRay "Republic" means "no monarchy"
The means don't matter to this option
But IIRC, the European Court of Human Rights has ruled that they cannot be arbitrarily deprived of their personal property; I don't know which properties they own personally and which are owned by the Crown
@lisamarsh Only men's football. If any of the UK members (England, Scotland, Wales and Northern Ireland) wins, that counts. If it exits the UK before winning, that doesn't count.