The most common and most likely answer to this crossword clue is the 8 letter word STILLEST
I've seen this crossword clue in The Guardian
S
T
I
L
L
E
S
T
More clues leading to the result STILLEST
Buddy explains!

The straight part
We know that "most unmoving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most unmoving = stillest.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 STILLEST mean?
STILLEST adjective- Not moving; calm.
- Not effervescing; not sparkling.
- Uttering no sound; silent.
- Having the same stated quality continuously from a past time
- Comparatively quiet or silent; soft; gentle; low.
- Constant; continual.