Crossword Genius

The one who deserted from the regiment on Tuesday? (3)

Ross

I believe the answer is:

rat

I'm a little stuck... Click here to teach me more about this clue!

'the one who deserted from' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'regiment on tuesday?' is the wordplay.
'regiment' becomes 'RA' (Royal Artillery).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'tuesday?' becomes 't'.
'ra'+'t'='RAT'

'the' acts as a link.

Can you help me to learn more?

(Other definitions for rat that I've seen before include "Betrayer" , "Treacherous rodent" , "one escaping doomed vessel?" , "Abandon" , "Domestic rodent" .)

I've seen this clue in the Evening Standard.
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