Not so much a sweetheart as pretty shrewd (4)
I believe the answer is:
cute
'pretty shrewd' is the definition.
'cute' can be an answer for 'shrewd' (I've seen this before). I am not certain of the 'pretty' bit.
'not so much a sweetheart' is the wordplay.
'not so much' becomes 'cut' (I can't justify this - if you can you should believe this answer much more).
'a sweetheart' becomes 'e' (the heart/centre of 'sweet').
'cut'+'e'='CUTE'
'as' acts as a link.
Can you help me to learn more?
(Other definitions for cute that I've seen before include "Shrewd" , "Astute - lovely" , "Endearingly pretty" , "Quaintly pleasing" , "Fly" .)