Heads rolling in “hire and fire” will produce such anger (3)

I believe the answer is:

ire

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'anger' is the definition.
(ire is intense rage)

I cannot understand how the remainder of the clue works.

(Other definitions for ire that I've seen before include "Annoyance, vexation" , "Outrage" , "Intense anger" , "'Anger, wrath (3)'" , "Strong emotion" .)

I've seen this clue in The Times.

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