The most common and most likely answer to this crossword clue is the 11 letter word ADVERTISING
I've seen this crossword clue in The Daily Telegraph
A
D
V
E
R
T
I
S
I
N
G
More clues leading to the result ADVERTISING
Buddy explains!

The straight part
We know that "Pushing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pushing = advertising.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 ADVERTISING mean?
ADVERTISING verb- To give (especially public) notice of (something); to announce publicly.
- To provide information about a person or goods and services to influence others.
- To provide public information about (a product, service etc.) in order to attract public awareness and increase sales.
- To notify (someone) of something; to call someone's attention to something.
- In gin rummy, to discard a card of one's preferred suit so as to mislead the opponent into thinking you do not want it.
- Communication whose purpose is to influence potential customers about products and services.
- The industry or profession made up of such communications.