[1] In 2004, Kleiter made her stage debut as Pamina in Mozart's Die Zauberflöte at the Opéra Bastille in Paris, conducted by Jiří Kout.

[3] Kleiter first appeared as Giunia in Johann Christian Bach's Lucio Silla in Winterthur, which led to continued work with the Zurich Opera, where she has appeared as Ilia in Mozart's Idomeneo, as Serpetta in his La finta giardiniera, conducted by Nicolaus Harnoncourt, as Sophie in Der Rosenkavalier by Richard Strauss, as Zdenka in his Arabella, conducted by Franz Welser-Möst, as Donna Elvira in Mozart's Don Giovanni in 2013, as Countess Almaviva in his Le nozze di Figaro in 2014 and as Fiordiligi in his Così fan tutte in 2016.

[3] She appeared as Susanna in Figaro in Verona, Reggio Emilia and Paris, and as Celia in Mozart's Lucio Silla conducted by Tomáš Netopil at La Fenice in Venice and at the 2006 Salzburg Festival.

[6] She recorded Bach's cantata Wachet auf, ruft uns die Stimme, BWV 140, conducted by Harnoncourt in 2007, live at the Musikverein in Vienna, with the Arnold Schoenberg Chor and the Concentus Musicus Wien, alongside Elisabeth von Magnus, Kurt Streit and Anton Scharinger.

[7][8] In 2018, she recorded Bach's St John Passion and his Christmas Oratorio with the Bachchor Mainz, conducted by Ralf Otto.