If we define 'warrior monks' as the fighter who took a vow to monastic profession, the knights templer and the knights hospitaller in the High Middle Ages were their fine examples.

As for participation of the clergy into war in the Early Middle Ages, I wrote on some Anglo-Saxon and Anglo-Norman examples in In the TV show Vikings, specifically S4 E18, the Northumbrian king brings his personal Bishop to battle with him. He is fully armored, and seemingly expects to partake in battle. Was this a common practice for rulers at the time? Or was it just an embellishment for entertainment purposes?.

If we look at other regions out of the British Isles, this kind of practice could be observed in Ottonian and Salian Germany (Arnold 1989), and also, in Christianized Scandinavia, ex-homeland of the Vikings as well (Lund 2000).

References:

• Arnold, Benjamin. "German Bishops and their Military Retinues in the Medieval Empire," German History 7-2 (1989): 161-83. https://doi.org/10.1093/gh/7.2.161
• Lund, Niels. 'A Bishop in Arms: Absalon and leding'. In: Archbishop Absalon of Lund and his World, ed. Karsten Friis-Jensen & Inge Skovgaard-Petersen, pp. 9-19. Roskilde, 2000.
• Sneddon, Jonathan. "Historical Introduction: Warrior Bishops in the Middle Ages." Medieval Warfare 3, no. 2 (2013): 6-8. Accessed February 19, 2021. doi:10.2307/48578211.