The most common and most likely answer to this crossword clue is the 10 letter word VIVIPARITY
I've seen this crossword clue in Financial Times
V
I
V
I
P
A
R
I
T
Y
More clues leading to the result VIVIPARITY
Buddy explains!

The straight part
We know that "Not laying eggs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not laying eggs = viviparity.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.