Possessive person who'll succeed on time (5)
I believe the answer is:
Here is my best explanation:
'possessive' is the definition.
(I've seen this before)
'person who'll succeed on time' is the wordplay.
'person who'll succeed' becomes 'heir'.
'on' is a charade indicator (letters next to each other).
'time' becomes 't'.
'heir' put after 't' is 'THEIR'.