“The Tudors” will reign for another season on Showtime.Feevee cabler has greenlit production on a third cycle of the regal drama. Lensing will begin June 16 in Dublin, with the series slated to return next year. Jonathan Rhys Meyers will continue to star as King Henry VIII. “The Tudors” is “now a fixture for us at Showtime, and we’re on our way to completing the entire saga of all six wives of Henry VIII,” said Showtime entertainment prexy Robert Greenblatt. Renewal isn’t a surprise. “The Tudors” continues to pull in strong ratings for Showtime and generates positive media buzz. Morgan O’Sullivan, Ben Silverman, Teri Weinberg, Eric Fellner, Tim Bevan, Sheila Hockin and Michael Hirst are exec producers. Hirst created and writes the series.