The most common and most likely answer to this crossword clue is the 5 letter word ARECA
I've seen this crossword clue in The Times
A
R
E
C
A
More clues leading to the result ARECA
Buddy explains!

The straight part
We know that "Palm" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case palm = areca.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 ARECA mean?
ARECA noun- Any member of the genus Areca of about fifty species of single-stemmed palms in the family Arecaceae, found in humid tropical forests.