Start to search inside hollow part of tooth (4)
I believe the answer is:
cusp
'part of tooth' is the definition.
(cusp is a part of a tooth)
'start to search inside hollow' is the wordplay.
'start to' suggests taking the first letters.
'inside' means one lot of letters goes inside another.
'hollow' becomes 'cup' (cup can mean a hollow or cavity).
The initial letter of 'search' is 's'.
's' going within 'cup' is 'CUSP'.
(Other definitions for cusp that I've seen before include "Either point of a crescent moon" , "Turning point on which important developments depend" , "Horn of moon" , "Intersection of curves" , "One point of a crescent moon" .)