I Reincarnated as a Useless Noble Lady

Kirara, a modern-day Japanese high school girl who has lived her life as a "gal," suddenly finds herself in another world as Chelsea, a "failed young lady." Unaware of the common sense of aristocratic society, unfamiliar with the rules of reincarnation in another world, and with no allies due to her younger sister Jennifer's schemes, Kirara/Chelsea finds herself in a hopeless position. Nevertheless, she sets out to somehow turn the situation around. She seeks instruction from a tutor who is known for his strictness, and Chelsea overcomes the tutoring with her natural guts, and her reputation in high society skyrockets! She also becomes close with Crown Prince Valentino and those around him...!?

(Source: AlphaPolis, translated)