Except for that hard-hearted bighead (3)
I believe the answer is:
bar
'except for' is the definition.
(I've seen this in another clue)
'hard-hearted bighead' is the wordplay.
I cannot quite see how this works, but
'bighead' could be 'b' (the head letter of 'big') and 'b' is located in the answer.
The remaining letters 'ar' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
'that' is the link.
Can you help me to learn more?
(Other definitions for bar that I've seen before include "Length of wood or metal - drinking place" , "Counter; prevent" , "drinking establishment" , "Iron rod or drinks counter" , "Batten" .)