From 1984 to 1995, Slaje was employed at the University Library of Graz as a subject specialist for Oriental Languages and Cultures and as head of the collection of scientific estates.
From October 1995 until his retirement in September 2019, he taught as tenured full professor of Indology at the Martin Luther University Halle-Wittenberg.
In 2000, he was elected to the Administrative Board of the Helmuth von Glasenapp Foundation (Mainz), which he has chaired since 2020.
Until its closure (2020) he acted as Director of the Centre for Historiography and Intellectual Culture of Kashmir established by the Academy of Sciences and Literature (Mainz) at the University of Halle.
From 1998 to 2009, he was the editor of the Indology section of the Zeitschrift der Deutschen Morgenländischen Gesellschaft (ZDMG).