Crescent point (4)
I believe the answer is:
cusp
'crescent point' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for cusp that I've seen before include "Pointed end - division between signs of the zodiac" , "Pointed end where two curves meet" , "Turning point on which important developments depend" , "Point where two curves meet - point of transition" , "Point where two arcs intersect arcs" .)