Swimming tutor upset about a bighead (6)

I believe the answer is:

turbot

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'swimming' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

'tutor upset about a bighead' is the wordplay.
'upset' is an anagram indicator.
'about' is an insertion indicator.
'a bighead' becomes 'b' (the head letter of 'big').
'tutor' with letters rearranged gives 'turot'.
'turot' going around 'b' is 'TURBOT'.

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(Other definitions for turbot that I've seen before include "Large food fish" , "Rub tot out with the fish" , "Edible flatfish" , "Species of flatfish" , "Flatfish - trout B (anag)" .)

I've seen this clue in the Evening Standard.

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