Fish a hat out for a student (7)

I believe the answer is:

bloater

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'fish' is the definition.
(bloater is a kind of fish)

I cannot understand how the remainder of the clue works.

(Other definitions for bloater that I've seen before include "Cured herring" , "Fish" , "Herring salted and smoked" , "Buckling" , "Something fishy" .)

I've seen this clue in the Evening Standard.

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