Cautiously shrewd about hard-heartedness (6)
I believe the answer is:
warily
'cautiously' is the definition.
(I've seen this in another clue)
'shrewd about hard-heartedness' is the wordplay.
'shrewd' becomes 'wily' (I've seen this before).
'about' means one lot of letters goes inside another.
'hard-heartedness' becomes 'ar' (I can't justify this - if you can you should believe this answer much more).
'wily' enclosing 'ar' is 'WARILY'.
Can you help me to learn more?
(Other definitions for warily that I've seen before include "with caution!" , "In a cautious manner" , "With circumspection" .)