Achieve one's ambitions (7)
I believe the answer is:
succeed
'achieve one's ambitions' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for succeed that I've seen before include "Do very well" , "Come after or achieve a goal" , "Take the place previously occupied by - be a winner" , "Achieve one's ambitions" , "Achieve the desired result" .)