The most common and most likely answer to this crossword clue is the 4 letter word LIMB
I've seen this crossword clue in The Times
L
I
M
B
More clues leading to the result LIMB
- Skinned shins and arm?
- Branch scale not Celsius
- Go up, cutting first bit off branch of tree
- Branch grasped by climber
- Member given rise Charlie rejected
- Member left Bengali film club at last
- Heading off to scale this part of tree
- Millions pocketed by former party member
- See 11ac.
- Branch to ascend, not reaching the top
Buddy explains!

The straight part
We know that "Branch" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case branch = limb.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 LIMB mean?
LIMB noun- A major appendage of human or animal, used for locomotion (such as an arm, leg or wing).
- A branch of a tree.
- The part of the bow, from the handle to the tip.
- An elementary piece of the mechanism of a lock.
- A thing or person regarded as a part or member of, or attachment to, something else.
- The part of a corolla beyond the throat.
- To remove the limbs from (an animal or tree).
- To supply with limbs.
- The apparent visual edge of a celestial body.
- (on a measuring instrument) The graduated edge of a circle or arc.
- The border or upper spreading part of a monopetalous corolla, or of a petal or sepal; blade.