Hard-core issue of incendiary crime (5)
I believe the answer is:
arson
'incendiary crime' is the definition.
(I've seen this before)
'hard-core issue' is the wordplay.
'core' says to take the centre.
'issue' becomes 'son' (issue can mean someone's offspring).
The central letters of 'hard' are 'ar'.
'ar'+'son'='ARSON'
'of' is the link.
(Other definitions for arson that I've seen before include "Fire requiring forensic study" , "Malicious fire-raising" , "Incendiary crime" , "Malicious fire-lighting" , "Criminal burning of property" .)