Born in Tartu, Vestmann studied choral direction from 1992 to 1996 at the Estonian Academy of Music and Theatre in Tallinn.
He was subsequently employed as a conductor at the Vanemuine theatre and opera house in Tartu, southern Estonia.
From 2000 to 2002, he studied with Wolf-Dieter Hauschild at the Hochschule für Musik Karlsruhe.
[2] In 2004/2005, Vestmann was General Music Director at the Vanemuine Theatre and Opera House in Tartu.
Since September 2006, Vestmann has been first Kapellmeister and deputy general music director at the Städtische Bühnen Münster.