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
1,000@TheAllMemeingEye well there is the supposed plot to install a ruler from the royal line of Jesus in some far future reality concocted by Pierre Plantard... not sure if that hits the mark.
Pierre Plantard de Saint-Clair was a French technical artist, best known for being the principal fabricator of the Priory of Sion hoax, by which he claimed from the 1960s onwards that he was a male-line Merovingian descendant of Dagobert II and the "Great Monarch" prophesied by Nostradamus. Today in France, he is commonly regarded as a con artist.
Seems like a trustworthy fella 👍