Involved in many different worlds, Elsa Moatti studied at the CNSM in Paris with Stéphanie-Marie Degand and Catherine Montier for the violin, and with Alexandros Markéas and Vincent Lê Quang for generative improvisation. She also studied at the Sibelius Academy in Helsinki with the violinist Réka Szilvay.

          She is involved in the world of creation and improvisation participating in productions with the Orchestre National de Jazz, the IRCAM, the ensemble Miroirs Etendus directed by Fiona Monbet, the Ensemble L'Itinéraire, Les 1000 et Une Nuits du Jazz at the Bal Blomet, Jacques Rebotier’s musical theatre company Voque and last but not least the improvisers’ collective La Croche-et-le-Marteau which she helped to found. She joined Le Concert Idéal directed by Marianne Piketty for the musical shows Vivaldi-Piazzolla, Fil d’Ariane, L’Heure Bleue and Vivaldi l’âge d’or, amongst others, all created at the Avignon festival between 2017 and 2021. She is involved in the world of theatre with the actress Emmanuelle Cordoliani, and with the director Xavier Lemaire in the show Madame Ming inspired by the novel by Eric-Emmanuel Schmitt. Elsa Moatti also plays early music, performing with ensembles such as Le Consort, Les Nouveaux Caractères, Les Talens Lyriques, and La Clique des Lunaisiens directed by Arnaud Marzorati.

          As a soloist, she has performed under the direction of Léo Margue, Gaël Péron and she regularly performs with the PSL orchestra conducted by Johan Farjot.

          In chamber music, she has played with the pianist Célia Oneto-Bensaïd with whom she was laureate of the Académie Ravel 2016, as well as with the pianist Michalis Boliakis and the cellist Juliette Salmona. With the pianist Suzanne Ben Zakoun, she forms a duo playing a repertoire ranging from classical to improvisation. In 2018, the Trio Hémisphères was born with the accordeonist Théo Ould and the double bassist Pierre-Antoine Despature, in a creative approach to a savant repertoire of popular origin.

          In 2022 she participated in the  OpusOne Academy of L’Itinéraire with the creation of her trio Rêvières. The same year she released her first CD Exiles under the Klarthe label. It has been acknowledged by press articles, in particular by Le Monde (portrait by Pierre Gervasoni, selected as one of the favorite CDs in 2022), Classica, and ClassiqueNews, and it led her to Jean-Baptiste Urbain’s microphone in  "La Matinale" of France Musique.

          Elsa Moatti is committed to teaching and holds a State Diploma and a Certificate of Proficiency in violin teaching. Since 2018, she has been teaching violin at the Maurice Ravel Conservatory in the 13th arrondissement of Paris.

          She plays a modern violin by Joël Klépal made in Paris in 2013 and baroque violin by Friedrich Meinel made in Germany in 1760.