The most common and most likely answer to this crossword clue is the 7 letter word RIBLESS
I've seen this crossword clue in The Guardian
R
I
B
L
E
S
S
Buddy explains!
The straight part
We know that "Like Adam, after Eve/Like Adam, after Eve" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like adam, after eve/like adam, after eve = ribless.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.