Old-school type, abrasive, leaving India (6)
I believe the answer is:
alumna
'old-school type' is the definition.
(female ex-pupil of a particular school)
'abrasive leaving india' is the wordplay.
'abrasive' becomes 'alumina' (alumina can be used as an abrasive).
'leaving' suggests deleting specific letters.
'india' becomes 'i' (phonetic alphabet: alpha, bravo, charlie etc.).
'alumina' with 'i' taken out is 'ALUMNA'.
(Other definitions for alumna that I've seen before include "She studied" , "Harvard graduate" , "Female graduate" , "Manual (anag) - old girl" , "Female former pupil" .)