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

The straight part
We know that "going astray" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case going astray = digressing.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.
Crossword Answer definitions
DIGRESSING verb- To step or turn aside; to deviate; to swerve; especially, to turn aside from the main subject of attention, or course of argument, in writing or speaking.
- To turn aside from the right path; to transgress; to offend.