Pressing desire, not heartless (6)
I believe the answer is:
urgent
'pressing' is the definition.
(I know that pressing can be written as urgent)
'desire not heartless' is the wordplay.
'desire' becomes 'urge' (I've seen this in another clue).
'heartless' says to hollow out the word (remove centre letters).
'not' with its centre removed is 'nt'.
'urge'+'nt'='URGENT'
(Other definitions for urgent that I've seen before include "Demanding immediate attention" , "Needing early action" , "Calling for immediate attention" , "Requiring early action" , "Important and in a hurry" .)