This is episode 66 of 82 of Doctor's Orders, Your Highness. Play it below, then continue straight into the next episode — the whole season is free and needs no account.
The closing stretch of the season, where the arc pays off.
A 21st-century doctor from a prestigious medical family transmigrates and decides to attach herself to the most powerful man available. He is a cold and ruthless prince who holds great power but suffers from a leg illness and despises women. She treats him, and he secretly wants to keep her close.