The most common and most likely answer to this crossword clue is the 10 letter word DEVOLUTION
I've seen this crossword clue in The Daily Telegraph
D
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More clues leading to the result DEVOLUTION
Buddy explains!

The straight part
We know that "delegation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case delegation = devolution.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 DEVOLUTION mean?
DEVOLUTION noun- A rolling down.
- A descent, especially one that passes through a series of revolutions, or by succession
- The transference of a right to a successor, or of a power from one body to another.
- Degeneration (as opposed to evolution).
- The transfer of some powers, and the delegation of some functions, from a central sovereign government to local government; eg. from Westminster to Scottish parliament and Welsh assembly.