Member of school got nurse in trouble (8)

I believe the answer is:

sturgeon

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'member of school' is the definition.
Although both the answer and definition are singular nouns, I don't see how one could define the other.

'got nurse in trouble' is the wordplay.
'in trouble' is an anagram indicator.
'got'+'nurse'='gotnurse'
'gotnurse' anagrammed gives 'STURGEON'.

Can you help me to learn more?

(Other definitions for sturgeon that I've seen before include "Fish producing caviare" , "supplier of delicacy" , "Fish sought for caviar" , "Fish - got nurse (anag)" , "Fish that yields caviare" .)

I've seen this clue in The Times and The Sunday Times.

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