The unending quarrel produced by project (5)
I believe the answer is:
throw
'project' is the definition.
('throw' can be a synonym of 'project')
'the unending quarrel produced by' is the wordplay.
'unending' means to remove the last letter.
'quarrel' becomes 'row' ('row' can be a synonym of 'quarrel').
'produced by' says to put letters next to each other.
'the' with its last letter removed is 'th'.
'th'+'row'='THROW'
(Other definitions for throw that I've seen before include "return from the boundary, perhaps" , "Deliberately lose" , "Light rug" , "Cast; give (party)" , "blanket" .)