Important desire not to lose heart (6)
I believe the answer is:
urgent
'important' is the definition.
(I've seen this before)
'desire not to lose heart' is the wordplay.
'desire' becomes 'urge' (I've seen this in another clue).
'to lose heart' means to remove the middle letters (I've seen 'losing heart' mean this).
'not' with its middle taken out is 'nt'.
'urge'+'nt'='URGENT'
(Other definitions for urgent that I've seen before include "Pressing, imperative" , "Pressing, compelling" , "High priority" , "Critical" , "Calling for immediate attention" .)