The most common and most likely answer to this crossword clue is the 8 letter word FLAGSHIP
I've seen this crossword clue in The Daily Telegraph
F
L
A
G
S
H
I
P
More clues leading to the result FLAGSHIP
- Leading institution marks joint suitable for replacement?
- Fellow falls behind in important vessel
- /23 Victory line, maybe, such as May’s shelved grammar school plan?
- Joint on tires is a thing of some importance
- Chief one in group indicates joint
- France falls behind fashionable joint leader of fleet
- Leading project? Female falls behind with it
- Fellow doesn’t keep up with trendy leading example
- Important part of body tires first
- Chief one in group points out joint
Buddy explains!

The straight part
We know that "Leading project" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case leading project = flagship.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 FLAGSHIP mean?
FLAGSHIP noun- (maritime) The ship occupied by the fleet's commander (usually an admiral); it denotes this by flying his flag.
- (maritime) The ship regarded as most important out of a group, e.g. a nation's navy or company's fleet.
- (by extension) The most important one out of a related group.
- To act as a flagship for