The most common and most likely answer to this crossword clue is the 15 letter word DRAUGHTSMANSHIP
I've seen this crossword clue in The Times
D
R
A
U
G
H
T
S
M
A
N
S
H
I
P
More clues leading to the result DRAUGHTSMANSHIP
Buddy explains!
The straight part
We know that "Skill in visualising/successful movement of men on board" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case skill in visualising/successful movement of men on board = draughtsmanship.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.