Rejects, with no new projections (5)
I believe the answer is:
spurs
'projections' is the definition.
(spur is a kind of projection)
'rejects with no new' is the wordplay.
'rejects' becomes 'spurns' ('spurn' can be a synonym of 'reject').
'with no' is a deletion indicator.
'new' becomes 'n'.
'spurns' with 'n' removed is 'SPURS'.
(Other definitions for spurs that I've seen before include "Kicks out" , "One side of London" , "soccer team" , "is stimulating" , "Goads" .)