Crossword Genius

His mate lays one decrepit redhead off (4)

Ross

I believe the answer is:

cock

'his mate lays' is the definition.
(a cock's mate is a hen, a layer of eggs)

'one decrepit redhead off' is the wordplay.
'one decrepit' becomes 'crock' (informal term for a very old person).
'redhead' becomes 'r' (the head/first letter of 'red').
'off' indicates named letters should be taken away.
'crock' with 'r' taken out is 'COCK'.

(Other definitions for cock that I've seen before include "Rooster" , "early bird" , "bull to > raise for shooting" , "Small heap of hay" , "Lift" .)

I've seen this clue in The Guardian.
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