Young widow Anna Leonowens goes to Thailand in 1861 to tutor the many children of King Mongkut. Their culture clash results in romantic sparks, and they fall in love.
Or, with barely any tweaking at all, it can be played as two strong-willed people developing a non-romantic friendship based on mutual respect.
Which, by the way, was the case in the original novel, Anna and the King of Siam (1944), based on the memoirs of the real Anna Leonowens: she became language secretary to King Mongkut, but didn't fall in love with the man 40 years her elder, and in fact found him unpleasant to work with. She had quit her job and was on her way back to England when he died.
Also, the King and his son Chulalongkorn are usually portrayed shirtless, so they'll be looking to cast the actors with the most smooth, muscular chests they can find.
Sometimes the actors go for the full Yul Brynner effect and shave their heads, too. Sometimes not.