rule with a rod of iron

To rule, govern, or control a group or population with complete power over all aspects of life, work, etc. He rules with a rod of iron, and moves swiftly to gain control over any entity that is not already in his grasp. She has ruled this company with a rod of iron for three decades, and it's going to be difficult for her to let go of control.

rule with an iron hand

To rule, govern, or control a group or population with complete, typically tyrannical authority over all aspects of life, work, etc. A noun or pronoun can be used between "rule" and "with." He rules with an iron hand, and moves swiftly to gain control over any entity that is not already in his grasp. She has ruled this company with an iron hand for three decades, and it's going to be difficult for her to let go of control.

rule (somebody/something) with a rod of ˈiron/with an iron ˈhand

(informal) control somebody/something in a very strong or strict way: They ruled the country with an iron hand and anybody who protested was arrested.

rule with a rod of iron/with an iron hand