Only son entering project (4)
I believe the answer is:
just
'only' is the definition.
('just' can be a synonym of 'only')
'son entering project' is the wordplay.
'son' becomes 's'.
'entering' means one lot of letters goes inside another.
'project' becomes 'jut' (I've seen this before**).
's' put inside 'jut' is 'JUST'.
(Other definitions for just that I've seen before include "Barely - deserved" , "Quite" , "Merited" , "Fair and proper" , "By a whisker" .)