The most common and most likely answer to this crossword clue is the 4 letter word PART
I've seen this crossword clue in Financial Times
P
A
R
T
More clues leading to the result PART
Buddy explains!

The straight part
We know that "Leave" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case leave = part.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 PART mean?
PART noun- A portion; a component.
- Duty; responsibility.
- The dividing line formed by combing the hair in different directions.
- In the Hebrew lunisolar calendar, a unit of time equivalent to 3⅓ seconds.
- A constituent of character or capacity; quality; faculty; talent; usually in the plural with a collective sense.
- To leave the company of.
- To cut hair with a parting; shed.
- To divide in two.
- To be divided in two or separated; shed.
- To divide up; to share.
- To have a part or share; to partake.
- To separate or disunite; to remove from contact or contiguity; to sunder.
- To hold apart; to stand or intervene between.
- To separate by a process of extraction, elimination, or secretion.
- To leave; to quit.
- To leave (an IRC channel).
- Fractional; partial.
- Partly; partially; fractionally.