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

The straight part
We know that "haul" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case haul = heave.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 HEAVE mean?
HEAVE noun- An effort to raise something, such as a weight or one's own body, or to move something heavy.
- An upward motion; a rising; a swell or distention, as of the breast in difficult breathing, of the waves, of the earth in an earthquake, etc.
- A horizontal dislocation in a metallic lode, taking place at an intersection with another lode.
- The measure of extent to which a nautical vessel goes up and down in a short period of time. Compare pitch.
- An effort to vomit; retching.
- (only used attributively as in "heave line" or "heave horse") Broken wind in horses.
- A forceful shot in which the ball follows a high trajectory
- To lift with difficulty; to raise with some effort; to lift (a heavy thing).
- To throw, cast.
- To rise and fall.
- To utter with effort.
- To pull up with a rope or cable.
- To lift (generally); to raise, or cause to move upwards (particularly in ships or vehicles) or forwards.
- To be thrown up or raised; to rise upward, as a tower or mound.
- To displace (a vein, stratum).
- To cause to swell or rise, especially in repeated exertions.
- To move in a certain direction or into a certain position or situation.
- To retch, to make an effort to vomit; to vomit.
- To make an effort to raise, throw, or move anything; to strain to do something difficult.
- To rob; to steal from; to plunder.