The most common and most likely answer to this crossword clue is the 11 letter word EXTRAPOLATE
I've seen this crossword clue in The Times
E
X
T
R
A
P
O
L
A
T
E
More clues leading to the result EXTRAPOLATE
- Highly courteous when one goes for a project
- Predict more staff will need to keep extremely alert
- Project inserting second bit of tooth into spare denture
- Unusually courteous, getting article for one — draw conclusions!
- Minor actor helping to win Oscar for project
- From available information draw conclusion to repeal tax changes
- Draw conclusion more work is sent up after hours
Buddy explains!

The straight part
We know that "project" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case project = extrapolate.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 EXTRAPOLATE mean?
EXTRAPOLATE verb- To infer by extending known information.
- To estimate the value of a variable outside a known range from values within that range by assuming that the estimated value follows logically from the known ones