The most common and most likely answer to this crossword clue is the 6 letter word LOGJAM
I've seen this crossword clue in The Times
L
O
G
J
A
M
More clues leading to the result LOGJAM
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The straight part
We know that "that’s not at all moving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s not at all moving = logjam.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 LOGJAM mean?
LOGJAM noun- An excess of logs being conveyed on a river, so that their motion halts.
- A clog or such jam or mess that halts or greatly delays progress.