Will's lady has project involving story (6)
I believe the answer is:
juliet
'will's lady' is the definition.
'Juliet' can be an answer for 'lady'. I'm unsure of the 'will's' bit.
'project involving story' is the wordplay.
'project' becomes 'jut' (I've seen this before).
'involving' indicates putting letters inside.
'story' becomes 'lie' (story can mean a fabrication).
'jut' placed around 'lie' is 'JULIET'.
'has' acts as a link.
Can you help me to learn more?
(Other definitions for juliet that I've seen before include "Romeo's lover" , "Miss 15" , "Play: 'Romeo and --'" , "See 2" , "Letter J in radio comms" .)