After grave message, enemy's beginning to be mature (4)
I believe the answer is:
ripe
'be mature' is the definition.
(synonyms)
'after grave message enemy's beginning' is the wordplay.
'after' means one lot of letters go next to another.
'grave message' becomes 'RIP' (rest in peace).
'beginning' indicates taking the first letters.
The first letter of 'enemys' is 'e'.
'rip' put next to 'e' is 'RIPE'.
'to' is the link.
(Other definitions for ripe that I've seen before include "daring" , "Mellow" , "Fully developed, ready to be eaten" , "Pier (anag.)" , "Ready for picking" .)