As much as we tend to think of separation of secular and ecclesiastical worlds in the middle ages, and that somehow monasteries and cathedrals were entirely 'staffed' and 'worked' by clergy, it isn't true and it helps us understand the answer to your question.

Monasteries from their earliest inceptions retained lay labourers (peasants) who either worked the lands for the abbey, or they received a benefice from the abbey which was then paid as rent in kind or cash. Or the abbey would have given a benefice to a noble who then owed rent or tribute of some sort. Moreover, bishops were very often both ecclesiastical leaders and lay lords who had minor nobility or peasantry working their lands, or again had given benefices.

The benefices may have come with worldly obligations like commitments to defence on the call of the lord (the levy). So, we have many instances where abbots and bishops, particularly in the 9-12th centuries, acting like lay lords in war. There are numerous examples of cartularies which record various bishops and abbots required to field a certain number knights (who again would themselves be under a lord who had benefices from the bishop, or themselves have a benefice), although not necessarily having to lead the army into battle.

This complicated relationship of lay and ecclesiastical lordship was a particular problem in the high medieval Holy Roman Empire, for the power in lay lordship which bishops and abbots held allowed Pope Gregory VII to challenge the German emperor Henry IV in 1075-1077 (as part of the 'Investiture Controversy'), effectively undermining Henry IV with an excommunication that had real teeth.

In the late 12th century, the emperor Barbarossa could invade Italy and wage war there with various bishops and abbots leading armies themselves composed of levies from bishop's lands. Here we can refer to Archbishop Christian von Mainz who brought an army to ravage Tuscany and then to assist Archbishop of Cologne Rainald von Dassel's 'shining knighthood' in their siege of Rome in 1167. We can also refer to Archbishop of Cologne Philip of Heinsberg who not only raised an army to wage war against Henry the Lion in Saxony, but also contracted the first known high medieval mercenary army with its infamous ravaging of the country side:

they robbed monasteries, burned churches, raped nuns, nothing and no one was spared, and above all ruthless looting and plundering.

In 1215 the Fourth Lateran Council forbade clergy from leading armies any longer, in word if not necessarily in fact.