Regarded as one of Iraq’s most skilled—if controversial—modern political operators, Sunni politician Mohammed Al-Halbousi has faced challenging times since his removal as parliament speaker in late 2023. Despite setbacks, he has managed to remain a key political figure, leveraging deft strategic maneuvering and carefully cultivated alliances to maintain influence.

When Sunni blocs were up in arms over a legal challenge last month to block the Sunni-sponsored General Amnesty Law, Halbousi...