The most common and most likely answer to this crossword clue is the 4 letter word PUSH
I've seen this crossword clue in The Daily Telegraph
P
U
S
H
More clues leading to the result PUSH
- Offensive street drawings that could get you going!
- Drive husband to drink, being contrary
- Press turn up, say nothing
- Illegally supply hard drink from the east
- Unpleasant substance found on hard drive
- Knock over hot drink
- Drive from hospital after discharge
- Promote in work, though not over hospital
- Hard drink, lifting elbow
- Press being offensive
Buddy explains!

The straight part
We know that "Press/being offensive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case press/being offensive = push.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 PUSH mean?
PUSH noun- A short, directed application of force; an act of pushing.
- An act of tensing the muscles of the abdomen in order to expel its contents.
- A great effort (to do something).
- An attempt to persuade someone into a particular course of action.
- A marching or drill maneuver/manoeuvre performed by moving a formation (especially a company front) forward or toward the audience, usually to accompany a dramatic climax or crescendo in the music.
- A wager that results in no loss or gain for the bettor as a result of a tie or even score
- The addition of a data item to the top of a stack.
- The situation where a server sends data to a client without waiting for a request.
- A particular crowd or throng or people.
- A foul shot in which the cue ball is in contact with the cue and the object ball at the same time
- To apply a force to (an object) such that it moves away from the person or thing applying the force.
- To continually attempt to persuade (a person) into a particular course of action.
- To press or urge forward; to drive.
- To continually promote (a point of view, a product for sale, etc.).
- To continually exert oneself in order to achieve a goal.
- To approach; to come close to.
- To tense the muscles in the abdomen in order to expel its contents.
- To continue to attempt to persuade a person into a particular course of action.
- To make a higher bid at an auction.
- To make an all-in bet.
- To move (a pawn) directly forward.
- To add (a data item) to the top of a stack.
- To publish (an update, etc.) by transmitting it to other computers.
- To thrust the points of the horns against; to gore.
- To burst out of its pot, as a bud or shoot.
- To strike the cue ball in such a way that it stays in contact with the cue and object ball at the same time (a foul shot).
- A pustule; a pimple.