Heart danger reduced chutzpah (6)
I believe the answer is:
hubris
'chutzpah' is the definition.
(I've seen this in another clue)
'heart danger reduced' is the wordplay.
'heart' becomes 'hub' (hub is a kind of heart).
'danger' becomes 'risk' (synonyms).
'reduced' means to remove the last letter.
'risk' with its last letter taken off is 'ris'.
'hub'+'ris'='HUBRIS'
(Other definitions for hubris that I've seen before include "The pride that goes before a fall" , "Irrational" , "having an extremely big head?" , "Arogant pride and egotism" , "show of arrogance" .)