The classical definition of a nation state requires territory, population, a formal body that can impose taxes and government policy, and recognition by (some number) of sovereign states. How does the last principle sit with regards to the right to self determination, which seems to be getting closer to becoming a peremptory norm?
The right of self-determination is typically a right of a "nation", i.e. a group of people who share a national identity (e.g. Kurds or Palestinians or Navajos or Kosovars or Scots) who are the dominant population of a compact and contiguous geographic area. Self-determination is a right that belongs to "peoples" not to states.
If you have a "nation state" then you have already achieved the self-determination to which you are entitled, which is another way of saying that you have a right to establish a sovereign state or in lieu of that, an autonomous region with substantially autonomous self-government.
How does the last principle sit with regards to the right to self determination
Well, if you get
territory, population, a formal body that can impose taxes and government policy, and recognition by (some number) of sovereign states
then you have the right to self determination, if you do not get them then you do not have that right1.
BTW, the requisites you mention are for the classical definition of an state, whatever it is a nation state or it is not.
1Maybe you could claim that you have the right but you are not allowed to use it, which reminds me much of this scene