Johann Hugo von Orsbeck finished his theological studies in 1655 and embarked on a two-month trip to Italy.

On January 7, 1672, the cathedral chapter of the Cathedral of Trier elected Johann Hugo von Orsbeck coadjutor Archbishop of Trier (alongside his uncle Karl Kaspar von der Leyen-Hohengeroldseck).

During the War of the Reunions, the Archbishopric of Trier was occupied by troops of the Kingdom of France in June and July 1684.

The French again invaded the archbishopric and the Bishopric of Speyer with the outbreak of the Nine Years' War in 1688.

On September 24, 1710, Orsbeck oversaw the election of Charles Joseph of Lorraine as his coadjutor and chosen successor.