Olga's Gallery has this writeup, "Nelidova, Ekaterina Ivanovna (1758-1839) - daughter of Lieutenant Ivan Dmitrievich Nelidov. She was raised in the Smolny Institute for Young Ladies and was noticed there by Empress Catherine II, who made her a maid of honor to the Grand Duchess Maria Feodorovna, later Empress, whose husband Emperor Pavel I was charmed by the grace and vivacity of Nelidova. She was sincerely attached to him, although their relations were never intimate. She was able to influence Pavel I, preventing some of his unwise decisions and tantrums. She was also a close friend of the Empress Maria Feodorovna."
She was one of several students of a young Ladies finishing school set up by Catherine II who were portrayed by Levitsky (this and the next two images), the Smolny Pupil Portraits. Kristina Aleksandrova of The St. Petersburg Times described the set of portraits in a review article here.