Earnest advocate has not lost heart (6)
I believe the answer is:
urgent
'earnest' is the definition.
(I've seen this before)
'advocate has not lost heart' is the wordplay.
'advocate' becomes 'urge' (synonyms).
'has' says to put letters next to each other.
'lost heart' means to remove the middle letters.
'not' with its middle taken out is 'nt'.
'urge'+'nt'='URGENT'
(Other definitions for urgent that I've seen before include "Demanding immediate attention" , "Important and in a hurry" , "Pressing, imperative" , "demanding speedy action" , "Requiring early action" .)