Change 'orse's 'eadgear? (5)

I believe the answer is:

alter

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''eadgear?' is the definition.
('halter' - thesaurus - said with the 'H' dropped, a cockney accent, like 'headgear' was)

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for alter that I've seen before include "Amend" , "Make changes to" , "Change, maybe later" , "reform" , "shift" .)

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