Director's left with instructor about to quit (5)

I believe the answer is:

loach

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

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for loach that I've seen before include "Fish with barbels around mouth" , "River fish - film director" , "Fish - British film director" , "Film-maker" , "Freshwater fish; rhymes with freshwater fish" .)

I've seen this clue in The Guardian.

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