After completing her secondary education, Kleinert embarked on an apprenticeship as a ceramic artisan. From 1987 to 1990, she attended the Hans Otto Theater School in Leipzig. Subsequently, she completed a two-year practical training at the "New Theater" in Halle. From 1991 to 1993, she had an engagement at the Brandenburg Theater.
Since 1993, Kleinert has been primarily known for her roles in television crime dramas. She has appeared as Eva Kowalski in several episodes of the series Sperling, as well as in Polizeiruf 110, Ein Fall für zwei, and Tatort, and has also been featured in the series Unser Lehrer Doktor Specht.
From 1999 to 2003, she played the role of Ellen Ludwig alongside Despina Pajanou in the RTL series Doppelter Einsatz. Since 2008, she has appeared in the series Mord mit Aussicht in the comical role of the curious police officer Heike Schäffer. Since 2013, she has portrayed the role of Sittenpolizistin Dagmar Schnee in the ZDF series SOKO Leipzig.