Cryptic crossword clue
New inlaw with wife missing, presumed dead? That’s awful

The most common and most likely answer to this crossword clue is the 3 plus 11 letter word NIL DESPERANDUM

I've seen this crossword clue in Financial Times
N
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Buddy explains!

The straight part
We know that "but don’t give up/! (3,11)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case but don’t give up/! (3,11) = nil desperandum.
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.

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