Shed a tear about girl's cleavage (6)
I believe the answer is:
cranny
'cleavage' is the definition.
(both can mean a cleft or opening)
'shed a tear about girl's' is the wordplay.
'shed a tear' becomes 'cry' (to cry is to shed tears).
'about' is an insertion indicator.
'girl' becomes 'ann' (woman's name).
'cry' enclosing 'ann' is 'CRANNY'.
(Other definitions for cranny that I've seen before include "Crack" , "Small rock fissure" , "corner" , "Fissure - chink" , "Crevice as hiding place" .)