The head of state/government can be of either a UN recognised nation or a defacto autonomous region.

The proclamation doesn't have to be official or definitely serious, them saying it on social media in a possibly humorous manner would count.

They must imply that they themselves are somehow part of the rightful dynastic succession rather than simply holding a different secular office that has rightfully replaced the dynasty.

A dynasty that has lost power but still has a widely recognised succession and presently active ceremonial title does not count as defunct e.g. the Oba of Benin. A dynasty that has lost power and has heavily unclear succession or has been formally abolished does count e.g. the Emperor of the Macedonian Empire.

A handful of examples of potential yes resolution scenarios:

• Donald Trump writes a Truth Social post calling himself the rightful emperor of the Roman Empire

• Emmanuel Macron mentions in an interview that he believes he is the rightful heir to the Bourbon monarchy of France

• Recep Erdogan declares in an open letter that he is the rightful caliph of Islam

• Xi Jinping starts referring to himself as the rightful heir to the Han Dynasty

• Claudia Scheinbaum starts saying she is rightful heir to the huey tlatoani of the Aztec Empire

• Vladimir Putin announces in a televised address that he is the Tsar of Russia as rightful heir to the Romanovs