The most common and most likely answer to this crossword clue is the 5 letter word CRAVE
I've seen this crossword clue in Financial Times
C
R
A
V
E
More clues leading to the result CRAVE
- Aspire to constant rapturous reception
- Long and yellow, with no tail
- Sigh for Conservative Party
- . Strongly desire potholer to take run-up
- Lust after Conservative Party
- Conservative party’s desire?
- Long for clubs to go wild
- Fancy redhead in Neanderthal’s place?
- Long for end to nationalistic party
- Longing to be less than totally cowardly
Buddy explains!

The straight part
We know that "Long for" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case long for = crave.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 CRAVE mean?
CRAVE noun- A formal application to a court to make a particular order.
- To desire strongly, so as to satisfy an appetite; to long or yearn for.
- To ask for earnestly; to beg; to claim.
- To call for; to require as a course of action.