Baldie snatching that lady's cigar (7)
I believe the answer is:
cheroot
'cigar' is the definition.
(cheroot is a kind of cigar)
'baldie snatching that lady's' is the wordplay.
'baldie' becomes 'coot' (as in the phrase 'bald as a coot').
'snatching' is an insertion indicator.
'that lady' becomes 'her' (her refers to a woman).
'coot' placed around 'her' is 'CHEROOT'.
(Other definitions for cheroot that I've seen before include "Type of cigar" , "16 21 [INDIAN IMPORT]" , "Square-cut cigar" , "Havana?" , "Cigar with open ends - hot core (anag)" .)