The sudden collapse of Bashar Al-Assad's government in Syria caught many by surprise, not least Iran’s allies in Iraq. As the Sunni Islamist Hayat Tahrir Al-Sham (HTS) advanced swiftly toward Damascus, Iraqi factions long active in defending the Syrian regime opted to stand down. Unlike during previous crises, neither these groups nor other foreign allies of Assad—including Russia, Iran and Lebanese Hezbollah—intervened.

The fall of Damascus on Dec. 7-8, just two weeks after the HTS-led offensive began, marks a significant shift in the regional balance of power. To Iraqi Shiite armed groups, the moment underscores a potential recalibration of...