The most common and most likely answer to this crossword clue is the 10 letter word RESILIENCE
I've seen this crossword clue in The Times
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Buddy explains!
The straight part
We know that "ability to recover" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ability to recover = resilience.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 RESILIENCE mean?
RESILIENCE noun- The mental ability to recover quickly from depression, illness or misfortune.
- The physical property of material that can resume its shape after being stretched or deformed; elasticity.
- The positive capacity of an organizational system or company to adapt and return to equilibrium due to the consequences of a crisis or failure caused by any type of disruption, including: an outage, natural disasters, man-made disasters, terrorism, or similar (particularly IT systems, archives).