The most common and most likely answer to this crossword clue is the 5 plus 5 letter word STOCK STILL
I've seen this crossword clue in Independent
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More clues leading to the result STOCK STILL
Buddy explains!
The straight part
We know that "not shifting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not shifting = stock still.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 STOCK STILL mean?
STOCK STILL adjective- Absolutely motionless, perfectly still.