The most common and most likely answer to this crossword clue is the 9 letter word INCENTIVE
I've seen this crossword clue in Financial Times
I
N
C
E
N
T
I
V
E
More clues leading to the result INCENTIVE
- One new coin setter has taken for carrot
- Stimulus of working in TV: nice to go over Eamonn’s head
- Carrot‘s nice in stew, throwing in turnip top and swede at the end
- Pinch 17 drivers, essentially, to get carrot
- Van Gogh heading off, given peeled carrot
- Carrot in a piece of American bread I have for afters
- Motivation to evict nine after redevelopment
- Motivation I have, following popular change in US
- At home with minimal cash, the setter has motivation
- It encourages popular change for Americans, I have to conclude
Buddy explains!

The straight part
We know that "carrot" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case carrot = incentive.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 INCENTIVE mean?
INCENTIVE noun- Something that motivates, rouses, or encourages.
- A bonus or reward, often monetary, to work harder.
- Inciting; encouraging or moving; rousing to action; stimulating.
- Serving to kindle or set on fire.