The most common and most likely answer to this crossword clue is the 11 letter word ABANDONMENT
I've seen this crossword clue in The Times
A
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Buddy explains!
The straight part
We know that "desertion" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case desertion = abandonment.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.
What does ABANDONMENT mean?
ABANDONMENT noun- The act of abandoning, or the state of being abandoned; total desertion; relinquishment.
- The voluntary leaving of a person to whom one is bound by a special relation, as a wife, husband or child; desertion.
- An abandoned building or structure.
- The relinquishment of a right, claim, or privilege; relinquishment of right to secure a patent by an inventor; relinquishment of copyright by an author.
- The relinquishment by the insured to the underwriters of what may remain of the property insured after a loss or damage by a peril insured against.
- The cessation of service on a particular segment of the lines of a common carrier, as granted by a government agency.
- A refusal to receive freight so damaged in transit as to be worthless and render carrier liable for its value.
- The self-surrender to an outside influence.
- Abandon; careless freedom or ease; surrender to one's emotions.