Crossword Genius

The opposite of hen, in a sense (4)

Ross

I believe the answer is:

stag

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'a sense' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

'the opposite of hen in' is the wordplay.
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'opposite of hen' becomes 'sag' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'in' means one lot of letters goes inside another.
't' put within 'sag' is 'STAG'.

Can you help me to learn more?

(Other definitions for stag that I've seen before include "Investor" , "Game - speculator" , "speculator wanting quick profit" , "in a rut, perhaps?" , "Horned animal" .)

I've seen this clue in the Evening Standard.
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