Rower or his headgear (6)

I believe the answer is:

boater

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'headgear' is the definition.
(I know that boater is a type of hat)

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

(Other definitions for boater that I've seen before include "Sailor's straw hat" , "Stiff hat made of straw" , "Hat; eg, rower" , "Hard flat straw hat, or person on water" , "Flat-topped straw hat" .)

I've seen this clue in The Mirror.

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