Pressing desire never to lose heart (6)
I believe the answer is:
urgent
'pressing' is the definition.
(I know that pressing can be written as urgent)
'desire never to lose heart' is the wordplay.
'desire' becomes 'urge' (I've seen this before).
'never' becomes 'not' (I've seen this in other clues).
'to lose heart' says to hollow out the word (remove centre letters) (I've seen 'losing heart' mean this).
'not' with its middle removed is 'nt'.
'urge'+'nt'='URGENT'
(Other definitions for urgent that I've seen before include "Requiring immediate action" , "Important and in a hurry" , "Requiring early action" , "High priority" , "Needing early action" .)