Puritan accepts rubbish project (8)
I believe the answer is:
protrude
'project' is the definition.
(synonyms)
'puritan accepts rubbish' is the wordplay.
'puritan' becomes 'prude' (synonyms).
'accepts' is an insertion indicator.
'rubbish' becomes 'rot' (both can mean nonsense).
'prude' enclosing 'rot' is 'PROTRUDE'.
(Other definitions for protrude that I've seen before include "Bulge" , "Stick out, project from a surface" , "Come out" , "Get through" , "Thrust forward" .)