The most common and most likely answer to this crossword clue is the 6 letter word NEWISH
I've seen this crossword clue in Financial Times
N
E
W
I
S
H
More clues leading to the result NEWISH
- Born abroad, want to be not too old
- Whines awfully having just been born
- Quite modern Tyneside institute mum joins
- Maybe Geordie wife injured his hip, to some extent
- Relatively recent Tyneside aspiration?
- When is building not much used?
- Fairly recent aspiration expressed inDurham?
- He wins awfully pretty novel
Buddy explains!

The straight part
We know that "having just been born" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having just been born = newish.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.