Chief Intendant and General of the cavalry, and his wife Marie née Princess of Sayn-Wittgenstein-Berleburg (1837–1920), a daughter of Carolyne zu Sayn-Wittgenstein, known for her liaison with Franz Liszt.

A confidant of the heir to the throne, Archduke Franz Ferdinand, he was appointed Minister-President of Cisleithania on 2 May 1906, in order to push through an electoral reform establishing universal male suffrage in elections to the Imperial Council, where his predecessor Paul Gautsch von Frankenthurn had failed.

Prince Konrad tried to mobilize the votes of the Italian representatives in the Council against a "Slavic" block, but did not succeed in achieving a majority.

As minister, he evolved plans of re-arranging the Austro-Hungarian dual monarchy into a federation of four major states: Austria proper, Hungary, Poland (Galicia), and "Illyria" (i.e. Croatia-Slavonia, Bosnia and Herzegovina, and Dalmatia).

[1] Together, they were the parents of six children, including:[2] Prince Konrad died on 21 December 1918 while hunting in Kammern im Liesingtal, Styria.