The most common and most likely answer to this crossword clue is the 10 letter word RETREATING
I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "Conceding defeat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case conceding defeat = retreating.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 RETREATING mean?
RETREATING verb- To treat or deal with (a topic) again or differently.
- To apply treatment to (an injury, a surface, etc.) again
- To withdraw from a position, go back.
- (of a glacier) To shrink back due to generally warmer temperatures.
- To slope back.
- The act of moving back from something; a retreat.