The most common and most likely answer to this crossword clue is the 6 letter word SCHEME
I've seen this crossword clue in The Guardian
S
C
H
E
M
E
More clues leading to the result SCHEME
- Plan second church straddling border
- School starts to employ more educational programme
- First couple from Scotland seen on border with English map
- Nietzsche meticulously hatching plot
- Plan for hiding revolutionary Frenchman in London area
- Cunning plan ?- stain at the front is to be removed from shirt
- Contrive to be seen in Porsche, mellowing
- Plan about border in south-east
- Second note about revolutionary plot
- Secretly plan to snare Charlie – he’s going out with yours truly
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 = scheme.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 SCHEME mean?
SCHEME noun- A systematic plan of future action.
- A plot or secret, devious plan.
- An orderly combination of related parts.
- A chart or diagram of a system or object.
- A type of geometric object.
- A council housing estate.
- An artful deviation from the ordinary arrangement of words.
- A representation of the aspects of the celestial bodies for any moment or at a given event.
- Part of a uniform resource identifier indicating the protocol or other purpose, such as http: or news:.
- A portfolio of pension plans with related benefits comprising multiple independent members.
- To plot, or contrive a plan.
- To plan; to contrive.