The most common and most likely answer to this crossword clue is the 3 letter word JAW
I've seen this crossword clue in The Times
J
A
W
More clues leading to the result JAW
Buddy explains!

The straight part
We know that "Gossip" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gossip = jaw.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 JAW mean?
JAW noun- One of the bones, usually bearing teeth, which form the framework of the mouth.
- The part of the face below the mouth.
- Anything resembling the jaw of an animal in form or action; especially plural, the mouth or way of entrance.
- A notch or opening.
- A notched or forked part, adapted for holding an object in place.
- One of a pair of opposing parts which are movable towards or from each other, for grasping or crushing anything between them.
- The inner end of a boom or gaff, hollowed in a half circle so as to move freely on a mast.
- Impudent or abusive talk.
- Axle guard.
- The curved part of the cushion marking the entry to the pocket.
- To assail or abuse by scolding.
- To scold; to clamor.
- To talk; to converse.
- (of a ball) To stick in the jaws of a pocket.
- (used in certain set phrases like jaw harp, jaw harpist and jaw's-trump)