A monarchist (supporter of monarchy) or supporter of a particular royal régime.
a supporter of the House of Bourbon, in France since the 18th century and especially during the French Revolution.
a supporter of Ferdinand VII of Spain in Spanish South America during the South American Wars of Independence of the 1810s and 1820s.
a Cavalier, a supporter of King Charles I of England during the English Civil War.
One who is resistant to change.