At the age of 3, she began playing the cello on a converted viola as a student of Margret Wortelmann at the Musikschule Bochum [de].
She received further instruction from Wolfgang Sellner, the solo cellist of the Bochumer Symphoniker, and Professor Wilfried Tachezi in Linz.
Gutzeit plays an original instrument by Gioffredo Cappa from 1677, which was made available to her by the Schulte-Uentrop Foundation.
Gutzeit made her debut as a soloist with the Pro Musica Orchestra Salzburg at the age of 12.
As a member of the "Clara Schumann Piano Trio" she has performed at the Salzburg Festival, the Rheingau Musik Festival, the Festspiele Mecklenburg-Vorpommern [de] and in Japan, and with this ensemble she has also won the Eduard-Söring-Prize of the Deutsche Stiftung Musikleben and the Classic Prize of the WDR and the City of Münster.