Important advocate not without heart (6)
I believe the answer is:
urgent
'important' is the definition.
(I've seen this before)
'advocate not without heart' is the wordplay.
'advocate' becomes 'urge' (synonyms).
'without heart' means to remove the middle letters.
'not' with its centre removed is 'nt'.
'urge'+'nt'='URGENT'
(Other definitions for urgent that I've seen before include "Extremely pressing" , "Pressing, compelling" , "demanding speedy action" , "Important and in a hurry" , "To be done asap" .)