The most common and most likely answer to this crossword clue is the 6 letter word STOLID
I've seen this crossword clue in Independent
S
T
O
L
I
D
More clues leading to the result STOLID
- Phlegmatic, firm about termination of contract
- Impassive girl many rejected
- It’s old liquid, hard to stir
- Uninspiring Tory leader enters firm
- Son informed about his heart is showing no emotion
- It’s old fashioned, wooden
- Almost nicked, I had to be emotionless
- Stone with offensive smell not likely to be moved
- Recalled points about line one being unemotional
- Impassive saint taking cover, hiding love
Buddy explains!

The straight part
We know that "not likely to be moved" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not likely to be moved = stolid.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 STOLID mean?
STOLID adjective- Having or revealing little emotion or sensibility; dully or heavily stupid.