Born in Hamburg,[1] Tetzlaff grew up in a pastor's household[2] with three siblings.

[2] She has also performed chamber music regularly with pianists including Leif Ove Andsnes, Alexander Lonquich, Lauma Skride, Gunilla Süssmann and with Lars Vogt who founded the Spannungen chamber music festival in Heimbach.

She has played with violinists including Baiba Skride and Antje Weithaas.

[2][5] Tetzlaff's repertoire is wide-ranging and also includes contemporary music of the 20th and 21st centuries, such as a CD with the cello concertos by Wolfgang Rihm and Ernst Toch.

[5] Since April 2024, Tetzlaff has been professor of cello and chamber music at the University of the Arts Bremen.