River Where the Moon Rises - it’s about a Goguryeo Princess. Kim So Hyun is the female lead. Focuses more on female lead’s journey but male lead is also an important main character and their chemistry is really amazing (especially since he was only the replacement male lead).
There’s also the movie about Princess Deokhye (one of the last princesses of Korea). Title is The Last Princess. Son Ye Jin plays the princess while Kim So Hyun plays her younger counterpart. Not romance centric, but it’s a good movie
Splendid Politics - I haven’t watched this but it’s about a Princess who lived through a turbulent period where there are a lot of changes in rulers. Lee Yeon Hee plays the female lead.