So basically, the girl (black hair) meets this (blond haired) boy and she made a promise to the boy that she would marry him, and also asked if he believed in reincarnation. She died in a car crash and got reincarnated, her and the boy eventually meet again and she tries to give the boy hints that she was the girl who died. I’m pretty sure they were in some fancy book place when they were younger too.
Jieum Ban has an extraordinary ability: she can remember the memories of all her past lives. After her previous life is cut short by a tragic accident, she sets out to reconnect with the people of her past life in her current one. Will memories of her 18th life sabotage romance in her 19th? Or will love endure across different lives?
The story focuses on the main character's 19th life as Jeium Ban, but starts with her 18th life, as a young woman with black hair named Juwon Wun. While visiting the house of her mother's friend, she meets the friend's son, Seoha.
This is likely the "fancy book place" in the question, but it's just part of their house. During this first meeting, she states that she has a secret and asks if he believes in past lives, but doesn't explicitly say that she remembers her past lives.
The promise to marry is there, but not very involved. Seoha basically blurts out "Let's get married!" and Juwon replies "sure".
After she dies in a car crash, she reincarnates and takes life more seriously in order to get a position at his family's company and reunite with him. She succeeds in doing this, but doesn't reveal that she's Juwon.