Part of tooth finally falls into mug (4)
I believe the answer is:
cusp
'part of tooth' is the definition.
('cusp' is part of 'tooth')
'finally falls into mug' is the wordplay.
'finally' indicates one should take the final letters.
'into' indicates putting letters inside.
'mug' becomes 'cup'.
The last letter of 'falls' is 's'.
's' put into 'cup' is 'CUSP'.
(Other definitions for cusp that I've seen before include "Turning point on which important developments depend" , "Pointed meeting of curves" , "Pointed end - division between signs of the zodiac" , "Point of transition, brink" , "Either point of a crescent moon" .)