Hesitate? Barber doesn't begin (5)

I believe the answer is:

haver

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'hesitate?' is the definition.
(I've seen this before)

I don't understand how the rest of the clue works.

(Other definitions for haver that I've seen before include "Act indecisively" , "Talk foolishly" , "Be indecisive" , "being with possessions?" , "show indecision" .)

I've seen this clue in The Telegraph.

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