'The Iron Lady', for example — hit Pete (anag) (7)

I believe the answer is:

epithet

(Other definitions for epithet that I've seen before include "The 23: an -- for Richard I" , "Descriptive term or short phrase" , "Descriptive term used to express a real quality" , "Descriptive adjective" , "Phrase expressing some quality of a person or thing" .)

I've seen this clue in The Guardian.

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