Crossword Genius

Eve welcoming half-cut Adam in for starters (5,4)

Ross

I believe the answer is:

first lady

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'eve' is the definition.
The definition and answer can be both people as well as being singular nouns.
Perhaps there's an association between them I don't understand?

'welcoming half-cut adam in for starters' is the wordplay.
'welcoming' means one lot of letters goes inside another (I've seen this in other clues).
'half cut' suggests halving the letters.
'in for starters' becomes 'firstly' (I can't justify this - if you can you should believe this answer much more).
'adam' halved is 'ad'.
'ad' put inside 'firstly' is 'FIRST LADY'.

Can you help me to learn more?

(Other definitions for first lady that I've seen before include "Twenty one [PRESIDENT]'s partner" , "Formerly, Jackie Kennedy for example" , "Title of American President's wife" , "Nancy, Barbara, Hillary or Laura?" , "top partner" .)

I've seen this clue in The Times.
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