The most common and most likely answer to this crossword clue is the 8 plus 8 plus 4 letter word ATLANTIC STANDARD TIME
I've seen this crossword clue in The Times
A
T
L
A
N
T
I
C
S
T
A
N
D
A
R
D
T
I
M
E
Buddy explains!
The straight part
We know that "In Barbados, say, how you’d get the measure of the enemy?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in barbados, say, how you’d get the measure of the enemy? = atlantic standard time.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.