Not voting to give to one's successors (4,4)
I believe the answer is:
hand down
'to one's successors' is the definition.
I can't tell whether this defines the answer.
'not voting to give' is the wordplay.
'not voting' becomes 'down' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'to' is a charade indicator (letters next to each other) (I've seen this in other clues).
'give' becomes 'hand' (synonyms).
'down' after 'hand' is 'HAND-DOWN'.
Can you help me to learn more?
(Another definition for hand down that I've seen is " Issue (judgment); bequeath".)