The most common and most likely answer to this crossword clue is the 8 letter word LEVANTER
I've seen this crossword clue in The Sunday Telegraph
L
E
V
A
N
T
E
R
More clues leading to the result LEVANTER
Buddy explains!

The straight part
We know that "strong easterly wind" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case strong easterly wind = levanter.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 LEVANTER mean?
LEVANTER noun- An Easterly wind that blows from the Mediterranean, through the straits of Gibraltar to the Atlantic.
- One who levants, or absconds to avoid paying a debt.