The most common and most likely answer to this crossword clue is the 10 letter word PERSUASION
I've seen this crossword clue in Financial Times
P
E
R
S
U
A
S
I
O
N
More clues leading to the result PERSUASION
Buddy explains!
The straight part
We know that "influence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case influence = persuasion.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 PERSUASION mean?
PERSUASION noun- The act of persuading, or trying to do so; the addressing of arguments to someone with the intention of changing their mind or convincing them of a certain point of view, course of action etc.
- An argument or other statement intended to influence one's opinions or beliefs; a way of persuading someone.
- A strongly held conviction, opinion or belief.
- One's ability or power to influence someone's opinions or feelings; persuasiveness.
- A specified religious adherence, a creed; any school of thought or ideology.
- (by extension, often humorous) Another personal, animal or inanimate trait that is not (very) liable to be changed by persuasion, such as sex, gender, ethnicity, origin, profession or nature.