Damo

Wang Won’s father is the king of Goryeo while his mother is the Yuan emperor’s daughter. He was born with many gifts as he has good looks, the wisdom of a snake, and a magnetic personality that draws people to him. But behind his gentle, virtuous demeanor, he has ambitions to conquer other lands. He has a faithful friend named Rin, who is a royal cousin and comrade with the same ambitions as he does. Then Wang Won has an encounter with a young woman named, San. San was someone that he recalled having met when he was a child and was lodged in his mind ever since. Wang Won sees how bright and confident San is and befriends her as well. But this friendship plants the seeds of tragedy. San’s beauty mesmerizes both Won and Rin and their seemingly strong bond start to fray over one woman

A historical drama featuring a star-crossed love triangle starring Ha Ji Won. The stories may be quite different but if you watched Empress Ki or Damo, and liked either of them really well, you must obviously have become a Ha Ji Won fan because since she's the lead of both shows. Therefore, I am recommending Damo to Empress Ki fans and Empress Ki to Damo fans. Both dramas feature Ha Ji Won as an orphan poor girl who has to overcome a lot of trials in her life. Both dramas are also her sageuks where she shows a lot of swordfighting and other action skills. Also in both shows, it appears that she had always loved a man who is kind and caring, but somehow became drawn to another man who she was not supposed to love. The love triangle in both dramas have great effects on Ha Ji Won's character since they both have/gave her something very important to her.
I suggests fans of either dramas watch the other since Ha Ji Won is fantastic in it. Also, because Damo was such a great drama for its time in 2003 but is somehow currently ignored because of so many newer dramas.

Ha Ji Won is the main character
She is also a police officer who chases the leader who made fake money
Both action period drama